1: Body Mass Index (BMI) on Hashimoto’s Thyroiditis (HT)

2: Waist to Hip Ratio (WHR) on Hashimoto’s Thyroiditis (HT)

3: Body Fat Percentage (BFP) on Hashimoto’s Thyroiditis (HT)

4: Waist Circumference (WC) on Hashimoto’s Thyroiditis (HT)

5: Hashimoto’s Thyroiditis (HT) on Body Mass Index (BMI)

6: Hashimoto’s Thyroiditis (HT) on Waist to Hip Ratio (WHR)

7: Hashimoto’s Thyroiditis (HT) on Body Fat Percentage (BFP)

8: Hashimoto’s Thyroiditis (HT) on Waist Circumference (WC)

BMI and HT

Introduction

  • Title: Investigating the causality between BMI on HT

Data Preparation

1- Number of total SNPs in exposure: 2,336,260 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 41,103 SNPs

3- Number of SNPs exposure after clumping : 521 SNPs

4- Number of total SNPs in outcome: 25,494,034 SNPs

5- Number of common variants between exposure and outcome: 498 SNPs

6- Number of SNPs after harmonization (action=2) = 498 SNPs

7- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 498 SNP

8- Number of SNPs after removing those that have MAF < 0.01 = 498 SNPs

9- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   28.62   37.43   50.41   70.27   73.13  822.78

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      UBrPan     E55MBv outcome exposure                  MR Egger  476
## 2      UBrPan     E55MBv outcome exposure           Weighted median  476
## 3      UBrPan     E55MBv outcome exposure Inverse variance weighted  476
## 4      UBrPan     E55MBv outcome exposure               Simple mode  476
## 5      UBrPan     E55MBv outcome exposure             Weighted mode  476
##           b         se         pval
## 1 0.5395003 0.18355992 3.452362e-03
## 2 0.3714829 0.09300390 6.489336e-05
## 3 0.3786296 0.06495165 5.562469e-09
## 4 0.3564533 0.28871708 2.175857e-01
## 5 0.3564533 0.17574059 4.308791e-02

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      UBrPan     E55MBv outcome exposure                  MR Egger 680.1400
## 2      UBrPan     E55MBv outcome exposure Inverse variance weighted 681.3999
##   Q_df       Q_pval
## 1  474 1.464060e-09
## 2  475 1.448661e-09
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      UBrPan     E55MBv outcome exposure    -0.002730524 0.002914015 0.3492195

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate         Sd   T-stat
## 1 beta.exposure               Raw       0.3786296 0.06495165 5.829407
## 2 beta.exposure Outlier-corrected       0.3984485 0.06039830 6.597016
##        P-value
## 1 1.028232e-08
## 2 1.123628e-10
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 684.0831
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<5e-05"
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##           RSSobs  Pvalue
## 1   2.796383e-04       1
## 2   1.489174e-06       1
## 3   2.066985e-05       1
## 4   8.105638e-05       1
## 5   1.326367e-04       1
## 6   9.632280e-04       1
## 7   4.730267e-06       1
## 8   3.488989e-06       1
## 9   1.123758e-03       1
## 10  1.067400e-05       1
## 11  2.857556e-04       1
## 12  3.609349e-05       1
## 13  2.191715e-03       1
## 14  5.285834e-04       1
## 15  2.145543e-05       1
## 16  2.839974e-04       1
## 17  3.813365e-04       1
## 18  1.309635e-06       1
## 19  6.648955e-09       1
## 20  1.738580e-07       1
## 21  3.385860e-06       1
## 22  6.210678e-06       1
## 23  3.292967e-04       1
## 24  9.216664e-07       1
## 25  9.118315e-05       1
## 26  1.597723e-04       1
## 27  4.203935e-04       1
## 28  1.493027e-03       1
## 29  6.053546e-04       1
## 30  1.122578e-03       1
## 31  8.240850e-05       1
## 32  3.302038e-05       1
## 33  8.896780e-07       1
## 34  2.129866e-05       1
## 35  7.419747e-05       1
## 36  6.741651e-04       1
## 37  3.220259e-04       1
## 38  4.377896e-04       1
## 39  3.883665e-04       1
## 40  1.910371e-05       1
## 41  2.825135e-02 <0.0238
## 42  2.772963e-03       1
## 43  2.042161e-04       1
## 44  1.014392e-05       1
## 45  4.514715e-04       1
## 46  2.696560e-04       1
## 47  1.603589e-06       1
## 48  5.430788e-04       1
## 49  9.224474e-04       1
## 50  1.641257e-05       1
## 51  4.315928e-03       1
## 52  4.517612e-04       1
## 53  7.444191e-04       1
## 54  1.514205e-04       1
## 55  6.655107e-04       1
## 56  2.569637e-04       1
## 57  2.678081e-03       1
## 58  8.960256e-06       1
## 59  1.071237e-03       1
## 60  7.981169e-06       1
## 61  1.757137e-04       1
## 62  3.950715e-05       1
## 63  8.576634e-06       1
## 64  1.290167e-03       1
## 65  8.222095e-06       1
## 66  1.526780e-04       1
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## 71  4.186285e-05       1
## 72  1.214443e-04       1
## 73  9.936022e-04       1
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## 75  2.560091e-03       1
## 76  3.963423e-03  0.6188
## 77  9.827956e-05       1
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## 79  1.261218e-04       1
## 80  1.038225e-04       1
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## 86  3.728104e-04       1
## 87  1.143034e-03       1
## 88  5.805511e-04       1
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## 90  2.862773e-04       1
## 91  3.153999e-04       1
## 92  1.298905e-04       1
## 93  3.087299e-04       1
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## 96  2.666651e-03       1
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## 100 1.282444e-04       1
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## 201 1.572053e-03       1
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## 204 1.242664e-06       1
## 205 2.774456e-05       1
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## 210 1.462788e-05       1
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## 212 1.666153e-03       1
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## 222 3.589691e-04       1
## 223 3.844340e-05       1
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## 225 3.574005e-03   0.238
## 226 3.388277e-09       1
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## 229 2.428777e-04       1
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## 239 1.605024e-03       1
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## 425 1.281693e-03       1
## 426 1.296385e-05       1
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## 428 1.491283e-03       1
## 429 3.471925e-04       1
## 430 1.165955e-03       1
## 431 1.733419e-05       1
## 432 2.968002e-04       1
## 433 4.962012e-04       1
## 434 3.501282e-05       1
## 435 1.331322e-04       1
## 436 4.373613e-06       1
## 437 4.269002e-04       1
## 438 9.238118e-05       1
## 439 4.077510e-05       1
## 440 6.739249e-05       1
## 441 2.386615e-04       1
## 442 1.768074e-04       1
## 443 1.515879e-04       1
## 444 1.042794e-04       1
## 445 7.924022e-04       1
## 446 3.050757e-04       1
## 447 2.952526e-04       1
## 448 9.838176e-04       1
## 449 3.232214e-03       1
## 450 8.850905e-04       1
## 451 2.413713e-04       1
## 452 1.312631e-04       1
## 453 3.512845e-04       1
## 454 4.375021e-04       1
## 455 2.552891e-05       1
## 456 3.147171e-04       1
## 457 1.181185e-04       1
## 458 3.953392e-04       1
## 459 3.650037e-04       1
## 460 1.788308e-03       1
## 461 7.320751e-04       1
## 462 3.379189e-05       1
## 463 1.866409e-04       1
## 464 2.580680e-03       1
## 465 2.165064e-03       1
## 466 5.412996e-04       1
## 467 3.076925e-04       1
## 468 1.935394e-04       1
## 469 1.395207e-04       1
## 470 2.062803e-05       1
## 471 8.302662e-06       1
## 472 3.316757e-06       1
## 473 1.156781e-05       1
## 474 1.427934e-05       1
## 475 5.908579e-05       1
## 476 3.351450e-04       1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 41
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##     -4.974029 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.7523
##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      UBrPan     E55MBv outcome exposure                  MR Egger  475
## 2      UBrPan     E55MBv outcome exposure           Weighted median  475
## 3      UBrPan     E55MBv outcome exposure Inverse variance weighted  475
## 4      UBrPan     E55MBv outcome exposure               Simple mode  475
## 5      UBrPan     E55MBv outcome exposure             Weighted mode  475
##           b         se         pval
## 1 0.5020618 0.17070766 3.431273e-03
## 2 0.3715559 0.09204898 5.425396e-05
## 3 0.3984485 0.06039830 4.195144e-11
## 4 0.3442747 0.26847127 2.003459e-01
## 5 0.3727984 0.17083094 2.958021e-02

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      UBrPan     E55MBv outcome exposure                  MR Egger 586.6165
## 2      UBrPan     E55MBv outcome exposure Inverse variance weighted 587.1389
##   Q_df       Q_pval
## 1  473 0.0002750681
## 2  474 0.0002925237
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      UBrPan     E55MBv outcome exposure    -0.001759702 0.002711426 0.5166566

Studentized residuals:

Radial test

## 
## Radial IVW
## 
##                   Estimate  Std.Error  t value     Pr(>|t|)
## Effect (Mod.2nd) 0.3984362 0.06039754 6.596895 4.198580e-11
## Iterative        0.3984362 0.06039754 6.596895 4.198580e-11
## Exact (FE)       0.4060776 0.05431601 7.476204 7.650038e-14
## Exact (RE)       0.4046144 0.05949561 6.800744 3.145262e-11
## 
## 
## Residual standard error: 1.112 on 474 degrees of freedom
## 
## F-statistic: 43.52 on 1 and 474 DF, p-value: 1.12e-10
## Q-Statistic for heterogeneity: 586.1241 on 474 DF , p-value: 0.0003250176
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Reference

##         41         63         74         81         88        118        125 
## 0.01460871 0.01753910 0.01087195 0.01429283 0.01456123 0.40736232 0.06002126 
##        142        153        155        163        178        181        188 
## 0.01467411 0.01443601 0.12452966 0.06141379 0.01328626 0.03837115 0.01479485 
##        208        210        245        297        385        401        463 
## 0.01362507 0.07437085 0.01804562 0.01440249 0.19920267 0.01083294 0.01651874

Run After deleting new outlier: Final Results:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      UBrPan     E55MBv outcome exposure                  MR Egger  445
## 2      UBrPan     E55MBv outcome exposure           Weighted median  445
## 3      UBrPan     E55MBv outcome exposure Inverse variance weighted  445
## 4      UBrPan     E55MBv outcome exposure               Simple mode  445
## 5      UBrPan     E55MBv outcome exposure             Weighted mode  445
##           b         se         pval
## 1 0.5220657 0.17100707 2.402946e-03
## 2 0.4042090 0.09318230 1.438959e-05
## 3 0.4225579 0.05777038 2.584608e-13
## 4 0.3806087 0.25202401 1.317017e-01
## 5 0.4088583 0.17553562 2.029603e-02

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      UBrPan     E55MBv outcome exposure                  MR Egger 421.2740
## 2      UBrPan     E55MBv outcome exposure Inverse variance weighted 421.6562
##   Q_df    Q_pval
## 1  443 0.7641431
## 2  444 0.7704410
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      UBrPan     E55MBv outcome exposure    -0.001631038 0.002638196 0.5367348

OR report:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      UBrPan     E55MBv outcome exposure                  MR Egger  445
## 2      UBrPan     E55MBv outcome exposure           Weighted median  445
## 3      UBrPan     E55MBv outcome exposure Inverse variance weighted  445
## 4      UBrPan     E55MBv outcome exposure               Simple mode  445
## 5      UBrPan     E55MBv outcome exposure             Weighted mode  445
##           b         se         pval       lo_ci     up_ci       or  or_lci95
## 1 0.5220657 0.17100707 2.402946e-03  0.18689185 0.8572396 1.685506 1.2054969
## 2 0.4042090 0.08759939 3.944404e-06  0.23251423 0.5759038 1.498117 1.2617684
## 3 0.4225579 0.05777038 2.584608e-13  0.30932791 0.5357878 1.525859 1.3625091
## 4 0.3806087 0.25388130 1.345428e-01 -0.11699869 0.8782160 1.463175 0.8895864
## 5 0.4088583 0.16499005 1.358001e-02  0.08547778 0.7322388 1.505098 1.0892374
##   or_uci95
## 1 2.356646
## 2 1.778737
## 3 1.708794
## 4 2.406602
## 5 2.079731

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 445 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.423     0.058 0.309, 0.536   0.000
## ------------------------------------------------------------------
## Residual standard error =  0.975 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 421.6562 on 444 degrees of freedom, (p-value = 0.7704). I^2 = 0.0%. 
## F statistic = 67.3.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.372     0.085   0.205 0.539   0.000
##            Weighted median    0.407     0.091   0.229 0.584   0.000
##  Penalized weighted median    0.396     0.091   0.218 0.573   0.000
##                                                                    
##                        IVW    0.423     0.058   0.309 0.536   0.000
##              Penalized IVW    0.413     0.058   0.300 0.527   0.000
##                 Robust IVW    0.400     0.053   0.297 0.503   0.000
##       Penalized robust IVW    0.399     0.052   0.297 0.501   0.000
##                                                                    
##                   MR-Egger    0.522     0.171   0.187 0.857   0.002
##                (intercept)   -0.002     0.003  -0.007 0.004   0.536
##         Penalized MR-Egger    0.520     0.171   0.184 0.856   0.002
##                (intercept)   -0.002     0.003  -0.007 0.003   0.521
##            Robust MR-Egger    0.515     0.131   0.259 0.771   0.000
##                (intercept)   -0.002     0.002  -0.006 0.003   0.403
##  Penalized robust MR-Egger    0.515     0.129   0.261 0.769   0.000
##                (intercept)   -0.002     0.002  -0.006 0.003   0.394

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
UBrPan E55MBv exposure outcome 0.065265 0.0012016 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.4288058
## 
## $beta.se
## [1] 0.05874331
## 
## $beta.p.value
## [1] 2.884359e-13
## 
## $naive.se
## [1] 0.05829219
## 
## $chi.sq.test
## [1] 420.8623
##   over.dispersion loss.function  beta.hat    beta.se
## 1           FALSE            l2 0.4288058 0.05874331
## 2           FALSE         huber 0.4084349 0.06025851
## 3           FALSE         tukey 0.4067305 0.06025774
## 4            TRUE            l2 0.4288054 0.05874593
## 5            TRUE         huber 0.4084349 0.06026027
## 6            TRUE         tukey 0.4067305 0.06025955
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  445 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.428 0.058  0.000 [0.314,0.542]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 445 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.429     0.059 0.314, 0.544   0.000  1398.109
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 445 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     MBE    0.409     0.194 0.028, 0.789   0.035
## ------------------------------------------------------------------

WHR and HT

Introduction

Data Preparation

1- Number of total SNPs in exposure: 2,560,781 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 544 SNPs

3- Number of SNPs exposure after clumping : 29 SNPs

4- Number of total SNPs in outcome: 25,660,792 SNPs

5- Number of common variants between exposure and outcome: 29 SNPs

7- Number of SNPs after harmonization (action=2) = 26 SNPs

8- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 26 SNP

9- Number of SNPs after removing those that have MAF < 0.01 = 26 SNPs

10- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   31.47   33.15   38.61   44.94   46.52  169.79

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      N6sC8E     lSRCpg outcome exposure                  MR Egger   26
## 2      N6sC8E     lSRCpg outcome exposure           Weighted median   26
## 3      N6sC8E     lSRCpg outcome exposure Inverse variance weighted   26
## 4      N6sC8E     lSRCpg outcome exposure               Simple mode   26
## 5      N6sC8E     lSRCpg outcome exposure             Weighted mode   26
##            b        se      pval
## 1 0.40677524 0.8481933 0.6358686
## 2 0.27930499 0.2227768 0.2099353
## 3 0.07395743 0.1832071 0.6864466
## 4 0.30551025 0.4494672 0.5029298
## 5 0.46986960 0.3368696 0.1753433

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      N6sC8E     lSRCpg outcome exposure                  MR Egger 39.56586
## 2      N6sC8E     lSRCpg outcome exposure Inverse variance weighted 39.83256
##   Q_df     Q_pval
## 1   24 0.02379768
## 2   25 0.03034011
##   id.exposure id.outcome outcome exposure egger_intercept         se      pval
## 1      N6sC8E     lSRCpg outcome exposure    -0.008596036 0.02137188 0.6910874

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate        Sd   T-stat   P-value
## 1 beta.exposure               Raw      0.07395743 0.1832071 0.403682 0.6898788
## 2 beta.exposure Outlier-corrected              NA        NA       NA        NA
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 43.1747
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.0342
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##          RSSobs Pvalue
## 1  9.493405e-09      1
## 2  1.897269e-03 0.4654
## 3  2.282802e-04      1
## 4  3.106932e-04      1
## 5  9.146917e-04      1
## 6  2.197246e-05      1
## 7  7.228149e-04      1
## 8  1.813512e-02   0.65
## 9  3.536541e-04      1
## 10 1.120301e-03      1
## 11 9.809659e-06      1
## 12 1.096665e-05      1
## 13 5.058903e-04      1
## 14 6.807367e-04      1
## 15 2.049507e-05      1
## 16 2.756644e-04      1
## 17 1.499848e-03 0.5486
## 18 5.610585e-05      1
## 19 5.921551e-04      1
## 20 3.796675e-03 0.1534
## 21 1.599047e-05      1
## 22 2.969934e-04      1
## 23 7.460494e-05      1
## 24 6.198409e-04      1
## 25 1.409228e-04      1
## 26 1.157995e-04      1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] "No significant outliers"
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## [1] NA
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] NA

Radial test

## 
## Radial IVW
## 
##                    Estimate Std.Error   t value  Pr(>|t|)
## Effect (Mod.2nd) 0.07395058 0.1832105 0.4036372 0.6864795
## Iterative        0.07395058 0.1832105 0.4036372 0.6864795
## Exact (FE)       0.07623916 0.1451601 0.5252076 0.5994389
## Exact (RE)       0.07537927 0.1832045 0.4114488 0.6842495
## 
## 
## Residual standard error: 1.262 on 25 degrees of freedom
## 
## F-statistic: 0.16 on 1 and 25 DF, p-value: 0.69
## Q-Statistic for heterogeneity: 39.82473 on 25 DF , p-value: 0.0303961
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"

Studentized residuals:

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Reference

##        8 
## 1.362547
## [1] 8

Run After deleting new outlier: Final Results:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      N6sC8E     lSRCpg outcome exposure                  MR Egger   13
## 2      N6sC8E     lSRCpg outcome exposure           Weighted median   13
## 3      N6sC8E     lSRCpg outcome exposure Inverse variance weighted   13
## 4      N6sC8E     lSRCpg outcome exposure               Simple mode   13
## 5      N6sC8E     lSRCpg outcome exposure             Weighted mode   13
##           b        se        pval
## 1 0.6201107 0.7591858 0.431371669
## 2 0.6668341 0.2570087 0.009470191
## 3 0.5840293 0.1934547 0.002536552
## 4 0.6274265 0.3864626 0.130439846
## 5 0.6779754 0.3428469 0.071416716

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      N6sC8E     lSRCpg outcome exposure                  MR Egger 3.287914
## 2      N6sC8E     lSRCpg outcome exposure Inverse variance weighted 3.290330
##   Q_df    Q_pval
## 1   11 0.9863476
## 2   12 0.9931240
##   id.exposure id.outcome outcome exposure egger_intercept         se      pval
## 1      N6sC8E     lSRCpg outcome exposure   -0.0009507916 0.01934515 0.9616817

OR report:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      N6sC8E     lSRCpg outcome exposure                  MR Egger   13
## 2      N6sC8E     lSRCpg outcome exposure           Weighted median   13
## 3      N6sC8E     lSRCpg outcome exposure Inverse variance weighted   13
## 4      N6sC8E     lSRCpg outcome exposure               Simple mode   13
## 5      N6sC8E     lSRCpg outcome exposure             Weighted mode   13
##           b        se        pval       lo_ci     up_ci       or  or_lci95
## 1 0.6201107 0.7591858 0.431371669 -0.86789348 2.1081149 1.859134 0.4198350
## 2 0.6668341 0.2722169 0.014299797  0.13328904 1.2003791 1.948060 1.1425802
## 3 0.5840293 0.1934547 0.002536552  0.20485817 0.9632005 1.793250 1.2273510
## 4 0.6274265 0.4070253 0.149144019 -0.17034320 1.4251961 1.872785 0.8433753
## 5 0.6779754 0.3345107 0.065500184  0.02233442 1.3336164 1.969885 1.0225857
##   or_uci95
## 1 8.232707
## 2 3.321376
## 3 2.620069
## 4 4.158673
## 5 3.794742

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 13 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.584     0.193 0.205, 0.963   0.003
## ------------------------------------------------------------------
## Residual standard error =  0.524 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 3.2903 on 12 degrees of freedom, (p-value = 0.9931). I^2 = 0.0%. 
## F statistic = 50.1.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.650     0.266   0.129 1.171   0.014
##            Weighted median    0.668     0.260   0.157 1.178   0.010
##  Penalized weighted median    0.668     0.260   0.157 1.178   0.010
##                                                                    
##                        IVW    0.584     0.193   0.205 0.963   0.003
##              Penalized IVW    0.584     0.193   0.205 0.963   0.003
##                 Robust IVW    0.601     0.179   0.250 0.951   0.001
##       Penalized robust IVW    0.601     0.179   0.250 0.951   0.001
##                                                                    
##                   MR-Egger    0.620     0.759  -0.868 2.108   0.414
##                (intercept)   -0.001     0.019  -0.039 0.037   0.961
##         Penalized MR-Egger    0.620     0.759  -0.868 2.108   0.414
##                (intercept)   -0.001     0.019  -0.039 0.037   0.961
##            Robust MR-Egger    0.704     0.508  -0.291 1.699   0.166
##                (intercept)   -0.003     0.013  -0.028 0.022   0.833
##  Penalized robust MR-Egger    0.704     0.508  -0.291 1.699   0.166
##                (intercept)   -0.003     0.013  -0.028 0.022   0.833

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
N6sC8E lSRCpg exposure outcome 0.0045076 3.14e-05 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.5879963
## 
## $beta.se
## [1] 0.2004967
## 
## $beta.p.value
## [1] 0.003360302
## 
## $naive.se
## [1] 0.1984777
## 
## $chi.sq.test
## [1] 3.238489
##   over.dispersion loss.function  beta.hat   beta.se
## 1           FALSE            l2 0.5879963 0.2004967
## 2           FALSE         huber 0.5879963 0.2057051
## 3           FALSE         tukey 0.5930146 0.2057561
## 4            TRUE            l2 0.5879964 0.2005585
## 5            TRUE         huber 0.5879963 0.2057687
## 6            TRUE         tukey 0.5930146 0.2058231
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  13 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.588 0.196  0.003 [0.204,0.972]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 13 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.596     0.199 0.206, 0.986   0.003   176.931
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 13 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.678     0.376 -0.059, 1.415   0.072
## ------------------------------------------------------------------

BFP and HT

Introduction

  • Title: Investigating the causality between BFP on HT

Data Preparation

1- Number of total SNPs in exposure: 9,837,128 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 50,635 SNPs

3- Number of SNPs exposure after clumping : 395 SNPs

4- Number of total SNPs in outcome: 25,494,034 SNPs

5- Number of common variants between exposure and outcome: 370 SNPs

7- Number of SNPs after harmonization (action=2) = 354 SNPs

8- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 354 SNP

9- Number of SNPs after removing those that have MAF < 0.01 = 354 SNPs

10- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   29.73   36.10   43.88   57.85   59.72  681.93

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      36OsIE     wtLUTb outcome exposure                  MR Egger  353
## 2      36OsIE     wtLUTb outcome exposure           Weighted median  353
## 3      36OsIE     wtLUTb outcome exposure Inverse variance weighted  353
## 4      36OsIE     wtLUTb outcome exposure               Simple mode  353
## 5      36OsIE     wtLUTb outcome exposure             Weighted mode  353
##             b         se         pval
## 1 -0.38507538 0.28537742 1.780928e-01
## 2 -0.45651283 0.12592743 2.887316e-04
## 3 -0.40325081 0.08844356 5.129653e-06
## 4  0.08978292 0.39322296 8.195256e-01
## 5 -0.65985411 0.30147982 2.927392e-02

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      36OsIE     wtLUTb outcome exposure                  MR Egger 476.1866
## 2      36OsIE     wtLUTb outcome exposure Inverse variance weighted 476.1927
##   Q_df       Q_pval
## 1  351 9.276022e-06
## 2  352 1.088141e-05
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      36OsIE     wtLUTb outcome exposure   -0.0002574515 0.003842707 0.9466219

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate        Sd    T-stat
## 1 beta.exposure               Raw      -0.4034657 0.0884239 -4.562857
## 2 beta.exposure Outlier-corrected              NA        NA        NA
##        P-value
## 1 6.974094e-06
## 2           NA
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 480.0678
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<4e-05"
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##           RSSobs  Pvalue
## 1   5.385832e-04       1
## 2   1.238476e-05       1
## 3   6.901517e-08       1
## 4   4.574568e-04       1
## 5   1.494669e-04       1
## 6   1.062879e-04       1
## 7   1.620091e-03       1
## 8   2.067088e-06       1
## 9   4.280177e-05       1
## 10  3.177953e-04       1
## 11  3.656414e-04       1
## 12  2.151977e-07       1
## 13  1.888113e-04       1
## 14  1.228239e-04       1
## 15  2.725863e-04       1
## 16  2.089499e-04       1
## 17  2.568255e-04       1
## 18  6.317205e-04       1
## 19  1.712762e-04       1
## 20  1.695643e-03       1
## 21  2.084410e-03       1
## 22  8.150654e-04       1
## 23  7.911814e-03 0.24072
## 24  2.608066e-05       1
## 25  1.474283e-04       1
## 26  2.097534e-03       1
## 27  1.177388e-04       1
## 28  6.044905e-05       1
## 29  1.250022e-03       1
## 30  1.884516e-04       1
## 31  2.141546e-04       1
## 32  2.781019e-04       1
## 33  2.809919e-04       1
## 34  4.586872e-04       1
## 35  1.317085e-04       1
## 36  3.877761e-04       1
## 37  8.714569e-05       1
## 38  4.657732e-03 0.65136
## 39  4.774082e-05       1
## 40  1.988448e-05       1
## 41  3.736142e-03       1
## 42  1.056856e-02       1
## 43  2.507428e-04       1
## 44  1.013546e-03       1
## 45  5.052449e-04       1
## 46  4.401590e-04       1
## 47  3.133794e-03 0.36816
## 48  1.918377e-03       1
## 49  3.624169e-04       1
## 50  8.132548e-04       1
## 51  9.455878e-04       1
## 52  4.784133e-05       1
## 53  1.551978e-04       1
## 54  4.609154e-04       1
## 55  2.174238e-05       1
## 56  7.930030e-07       1
## 57  8.488609e-04       1
## 58  1.457717e-03       1
## 59  3.635529e-03       1
## 60  3.396076e-04       1
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## 62  1.481503e-04       1
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## 64  6.605221e-03       1
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## 73  1.628751e-05       1
## 74  3.075929e-04       1
## 75  8.488777e-04       1
## 76  3.614562e-05       1
## 77  7.464952e-06       1
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## 79  4.321954e-04       1
## 80  8.002928e-02       1
## 81  2.871746e-04       1
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## 83  1.397378e-02       1
## 84  1.910520e-04       1
## 85  4.404306e-03       1
## 86  4.603459e-04       1
## 87  1.289582e-03       1
## 88  5.502000e-04       1
## 89  1.333071e-04       1
## 90  4.986577e-06       1
## 91  1.927893e-05       1
## 92  1.495549e-05       1
## 93  2.988037e-04       1
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## 96  4.909284e-05       1
## 97  1.075487e-04       1
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## 99  4.692347e-03       1
## 100 8.863803e-05       1
## 101 1.648156e-04       1
## 102 6.011365e-05       1
## 103 2.213554e-04       1
## 104 2.820969e-05       1
## 105 2.126244e-05       1
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## 107 1.631071e-04       1
## 108 3.531315e-03       1
## 109 6.433024e-04       1
## 110 4.282212e-04       1
## 111 5.226444e-04       1
## 112 4.288000e-04       1
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## 115 3.014965e-04       1
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## 126 2.065830e-04       1
## 127 1.803783e-05       1
## 128 9.972710e-05       1
## 129 2.873072e-04       1
## 130 1.895027e-04       1
## 131 8.839834e-04       1
## 132 2.333953e-04       1
## 133 1.485660e-03       1
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## 135 1.338099e-04       1
## 136 3.036417e-04       1
## 137 5.420606e-04       1
## 138 2.531832e-04       1
## 139 6.571967e-03       1
## 140 1.261776e-03       1
## 141 5.366611e-05       1
## 142 4.582412e-05       1
## 143 4.708773e-04       1
## 144 3.765589e-05       1
## 145 1.206024e-04       1
## 146 3.496485e-04       1
## 147 5.293662e-05       1
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## 149 2.007809e-04       1
## 150 1.249207e-04       1
## 151 2.211387e-04       1
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## 153 3.915991e-04       1
## 154 1.042955e-04       1
## 155 2.400686e-04       1
## 156 5.637806e-04       1
## 157 4.260249e-04       1
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## 159 3.495659e-03       1
## 160 4.107265e-04       1
## 161 1.617825e-03       1
## 162 1.433986e-03       1
## 163 8.469280e-04       1
## 164 5.948216e-05       1
## 165 8.010472e-07       1
## 166 1.201129e-04       1
## 167 1.852486e-04       1
## 168 8.334133e-06       1
## 169 1.687785e-04       1
## 170 1.219252e-03       1
## 171 2.264660e-04       1
## 172 3.257304e-04       1
## 173 1.019490e-04       1
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## 175 2.312613e-03       1
## 176 1.365065e-03       1
## 177 1.819388e-04       1
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## 179 5.401614e-04       1
## 180 3.193787e-04       1
## 181 1.457861e-05       1
## 182 4.917751e-03       1
## 183 1.413333e-04       1
## 184 8.294892e-04       1
## 185 3.841431e-03 0.16992
## 186 3.884947e-04       1
## 187 1.582834e-04       1
## 188 1.743990e-05       1
## 189 2.242004e-05       1
## 190 2.381734e-06       1
## 191 8.992970e-06       1
## 192 1.177123e-06       1
## 193 9.692614e-05       1
## 194 7.582926e-04       1
## 195 2.577297e-04       1
## 196 1.974810e-04       1
## 197 6.346329e-07       1
## 198 1.047515e-03       1
## 199 5.260702e-06       1
## 200 1.181735e-03       1
## 201 2.573004e-04       1
## 202 2.374709e-06       1
## 203 2.267669e-04       1
## 204 7.556554e-08       1
## 205 8.523758e-04       1
## 206 2.391252e-06       1
## 207 1.089931e-04       1
## 208 3.430813e-04       1
## 209 1.782120e-04       1
## 210 2.358251e-04       1
## 211 9.601126e-05       1
## 212 1.196473e-04       1
## 213 5.443957e-03   0.708
## 214 1.412227e-04       1
## 215 1.996955e-04       1
## 216 1.881587e-03       1
## 217 6.644281e-05       1
## 218 9.707838e-07       1
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## 220 1.748865e-04       1
## 221 5.924169e-04       1
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## 226 3.920643e-05       1
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## 249 1.232393e-03       1
## 250 4.265298e-04       1
## 251 1.744010e-05       1
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## 255 1.085345e-04       1
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## 259 3.855121e-04       1
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## 272 2.041131e-05       1
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## 276 2.200610e-04       1
## 277 2.119843e-04       1
## 278 4.144660e-07       1
## 279 9.081197e-06       1
## 280 8.762597e-03  0.0708
## 281 1.937506e-04       1
## 282 8.409166e-05       1
## 283 7.593366e-04       1
## 284 3.988484e-05       1
## 285 1.505631e-04       1
## 286 3.265736e-05       1
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## 290 4.160691e-03       1
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## 292 1.046082e-03       1
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## 296 1.320708e-04       1
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## 298 6.013164e-03       1
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## 300 2.960680e-05       1
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## 303 4.353270e-04       1
## 304 1.111063e-04       1
## 305 1.904520e-05       1
## 306 3.094016e-04       1
## 307 9.387204e-04       1
## 308 3.641070e-04       1
## 309 1.798854e-03       1
## 310 4.592932e-04       1
## 311 2.503222e-06       1
## 312 3.796377e-03       1
## 313 2.010689e-05       1
## 314 3.078660e-04       1
## 315 2.972342e-04       1
## 316 8.968042e-07       1
## 317 9.394070e-04       1
## 318 2.755109e-05       1
## 319 4.781835e-04       1
## 320 2.142499e-07       1
## 321 4.377816e-04       1
## 322 3.568346e-03       1
## 323 1.019549e-04       1
## 324 5.424727e-05       1
## 325 6.763159e-05       1
## 326 6.498877e-04       1
## 327 8.208781e-03       1
## 328 4.092829e-04       1
## 329 1.190227e-03       1
## 330 6.625285e-04       1
## 331 6.033625e-06       1
## 332 7.974648e-04       1
## 333 2.486397e-05       1
## 334 4.031754e-09       1
## 335 1.811816e-05       1
## 336 1.724188e-04       1
## 337 8.187141e-05       1
## 338 4.535710e-04       1
## 339 1.206100e-03       1
## 340 1.123762e-04       1
## 341 6.248245e-04       1
## 342 1.035878e-03       1
## 343 1.729371e-03       1
## 344 1.653988e-03       1
## 345 6.817376e-04       1
## 346 2.040774e-03       1
## 347 2.327309e-04       1
## 348 6.237500e-04       1
## 349 5.559586e-04       1
## 350 1.092376e-03       1
## 351 1.370136e-03       1
## 352 1.367958e-04       1
## 353 3.835279e-03 0.09912
## 354 6.012350e-05       1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] "No significant outliers"
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## [1] NA
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] NA

Radial test

## 
## Radial IVW
## 
##                    Estimate  Std.Error   t value     Pr(>|t|)
## Effect (Mod.2nd) -0.4034325 0.08842763 -4.562290 5.059867e-06
## Iterative        -0.4034325 0.08842763 -4.562290 5.059867e-06
## Exact (FE)       -0.4129634 0.07609809 -5.426725 5.739749e-08
## Exact (RE)       -0.4104574 0.08659467 -4.739984 3.104691e-06
## 
## 
## Residual standard error: 1.162 on 353 degrees of freedom
## 
## F-statistic: 20.81 on 1 and 353 DF, p-value: 6.99e-06
## Q-Statistic for heterogeneity: 476.6866 on 353 DF , p-value: 1.192346e-05
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"

Studentized residuals:

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Reference

##         41         42         59         64         80         83        108 
## 0.01990057 0.04748505 0.03529283 0.03339141 0.07589678 0.15680098 0.10893105 
##        139        182        225        241        247        280        287 
## 0.02548446 0.04794978 0.47130068 0.09831783 0.01744461 0.05158769 0.14978191 
##        327 
## 0.10494023
##  [1]  23  42  64  80  83  99 120 139 182 213 225 241 280 287 298 327

Run After deleting new outlier: Final Results:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      36OsIE     wtLUTb outcome exposure                  MR Egger  318
## 2      36OsIE     wtLUTb outcome exposure           Weighted median  318
## 3      36OsIE     wtLUTb outcome exposure Inverse variance weighted  318
## 4      36OsIE     wtLUTb outcome exposure               Simple mode  318
## 5      36OsIE     wtLUTb outcome exposure             Weighted mode  318
##             b         se         pval
## 1 -0.58585178 0.32202357 6.981461e-02
## 2 -0.44999521 0.13013533 5.443995e-04
## 3 -0.48269876 0.08464925 1.181743e-08
## 4 -0.01000789 0.38896443 9.794892e-01
## 5 -0.54229425 0.29714007 6.893505e-02

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      36OsIE     wtLUTb outcome exposure                  MR Egger 283.0949
## 2      36OsIE     wtLUTb outcome exposure Inverse variance weighted 283.2051
##   Q_df    Q_pval
## 1  316 0.9083303
## 2  317 0.9140844
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      36OsIE     wtLUTb outcome exposure     0.001363986 0.004108351 0.7401068

OR report:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      36OsIE     wtLUTb outcome exposure                  MR Egger  318
## 2      36OsIE     wtLUTb outcome exposure           Weighted median  318
## 3      36OsIE     wtLUTb outcome exposure Inverse variance weighted  318
## 4      36OsIE     wtLUTb outcome exposure               Simple mode  318
## 5      36OsIE     wtLUTb outcome exposure             Weighted mode  318
##             b         se         pval      lo_ci       up_ci        or
## 1 -0.58585178 0.32202357 6.981461e-02 -1.2170180  0.04531442 0.5566315
## 2 -0.44999521 0.12136949 2.091942e-04 -0.6878794 -0.21211100 0.6376312
## 3 -0.48269876 0.08464925 1.181743e-08 -0.6486113 -0.31678622 0.6171157
## 4 -0.01000789 0.38788728 9.794323e-01 -0.7702670  0.75025118 0.9900420
## 5 -0.54229425 0.30926717 8.048587e-02 -1.1484579  0.06386940 0.5814128
##    or_lci95  or_uci95
## 1 0.2961119 1.0463568
## 2 0.5026408 0.8088749
## 3 0.5227713 0.7284865
## 4 0.4628895 2.1175318
## 5 0.3171254 1.0659532

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 319 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI        p-value
##     IVW   -0.483     0.085 -0.649, -0.317   0.000
## ------------------------------------------------------------------
## Residual standard error =  0.946 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 284.3431 on 318 degrees of freedom, (p-value = 0.9128). I^2 = 0.0%. 
## F statistic = 52.8.
##                     Method Estimate Std Error 95% CI         P-value
##              Simple median   -0.428     0.126  -0.674 -0.181   0.001
##            Weighted median   -0.462     0.126  -0.709 -0.214   0.000
##  Penalized weighted median   -0.462     0.126  -0.710 -0.215   0.000
##                                                                     
##                        IVW   -0.483     0.085  -0.649 -0.317   0.000
##              Penalized IVW   -0.483     0.085  -0.649 -0.317   0.000
##                 Robust IVW   -0.480     0.078  -0.634 -0.326   0.000
##       Penalized robust IVW   -0.480     0.078  -0.634 -0.326   0.000
##                                                                     
##                   MR-Egger   -0.585     0.322  -1.216  0.047   0.069
##                (intercept)    0.001     0.004  -0.007  0.009   0.744
##         Penalized MR-Egger   -0.585     0.322  -1.216  0.047   0.069
##                (intercept)    0.001     0.004  -0.007  0.009   0.744
##            Robust MR-Egger   -0.627     0.249  -1.115 -0.138   0.012
##                (intercept)    0.002     0.003  -0.005  0.009   0.574
##  Penalized robust MR-Egger   -0.627     0.249  -1.115 -0.138   0.012
##                (intercept)    0.002     0.003  -0.005  0.009   0.574

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
36OsIE wtLUTb exposure outcome 0.0370296 0.0008009 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] -0.4911237
## 
## $beta.se
## [1] 0.08648412
## 
## $beta.p.value
## [1] 1.356642e-08
## 
## $naive.se
## [1] 0.08565622
## 
## $chi.sq.test
## [1] 283.7915
##   over.dispersion loss.function   beta.hat    beta.se
## 1           FALSE            l2 -0.4911237 0.08648412
## 2           FALSE         huber -0.4865283 0.08872731
## 3           FALSE         tukey -0.4882809 0.08872879
## 4            TRUE            l2 -0.4911235 0.08648876
## 5            TRUE         huber -0.4865283 0.08873101
## 6            TRUE         tukey -0.4882809 0.08873266
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  319 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue          95% CI
##  cML-MA-BIC   -0.491 0.085  0.000 [-0.659,-0.324]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 319 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI        p-value Condition
##    dIVW   -0.492     0.086 -0.662, -0.323   0.000   924.829
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 319 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE   -0.553     0.319 -1.178, 0.071   0.083
## ------------------------------------------------------------------

WC and HT

Introduction

  • Title: Investigating the causality between WC on HT

Data Preparation

1- Number of total SNPs in exposure: 10,545,186 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 20,221 SNPs

3- Number of SNPs exposure after clumping : 230 SNPs

4- Number of total SNPs in outcome: 25,660,792 SNPs

5- Number of common variants between exposure and outcome: 217 SNPs

7- Number of SNPs after harmonization (action=2) = 209 SNPs

8- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 209 SNP

9- Number of SNPs after removing those that have MAF < 0.01 = 209 SNPs

10- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   29.76   34.94   42.15   54.60   54.22  660.76

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      3BmkaS     MNE7VH outcome exposure                  MR Egger  208
## 2      3BmkaS     MNE7VH outcome exposure           Weighted median  208
## 3      3BmkaS     MNE7VH outcome exposure Inverse variance weighted  208
## 4      3BmkaS     MNE7VH outcome exposure               Simple mode  208
## 5      3BmkaS     MNE7VH outcome exposure             Weighted mode  208
##           b         se         pval
## 1 0.7300481 0.24080256 2.743720e-03
## 2 0.5039815 0.12500218 5.535555e-05
## 3 0.5017159 0.07837754 1.540882e-10
## 4 0.3932087 0.32459676 2.271324e-01
## 5 0.5257821 0.21480440 1.520918e-02

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      3BmkaS     MNE7VH outcome exposure                  MR Egger 237.0435
## 2      3BmkaS     MNE7VH outcome exposure Inverse variance weighted 238.2007
##   Q_df     Q_pval
## 1  206 0.06796049
## 2  207 0.06746991
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      3BmkaS     MNE7VH outcome exposure    -0.004416888 0.004404478 0.3171253

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate         Sd   T-stat
## 1 beta.exposure               Raw       0.5020184 0.07837133 6.405638
## 2 beta.exposure Outlier-corrected              NA         NA       NA
##        P-value
## 1 9.818503e-10
## 2           NA
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 241.5028
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.076

Radial test

## 
## Radial IVW
## 
##                   Estimate  Std.Error  t value     Pr(>|t|)
## Effect (Mod.2nd) 0.5020712 0.07838038 6.405572 1.498070e-10
## Iterative        0.5020712 0.07838038 6.405572 1.498070e-10
## Exact (FE)       0.5128747 0.07323148 7.003474 2.496930e-12
## Exact (RE)       0.5114683 0.07743077 6.605492 3.253484e-10
## 
## 
## Residual standard error: 1.07 on 208 degrees of freedom
## 
## F-statistic: 41.03 on 1 and 208 DF, p-value: 9.82e-10
## Q-Statistic for heterogeneity: 238.3229 on 208 DF , p-value: 0.07320178
## 
##  Outliers detected 
## Number of iterations = 2
##         SNP Q_statistic      p.value
## 1 rs7752202    15.58768 7.876623e-05
##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      3BmkaS     MNE7VH outcome exposure                  MR Egger  207
## 2      3BmkaS     MNE7VH outcome exposure           Weighted median  207
## 3      3BmkaS     MNE7VH outcome exposure Inverse variance weighted  207
## 4      3BmkaS     MNE7VH outcome exposure               Simple mode  207
## 5      3BmkaS     MNE7VH outcome exposure             Weighted mode  207
##           b         se         pval
## 1 0.7299790 0.24150166 2.825171e-03
## 2 0.5040355 0.12857250 8.845944e-05
## 3 0.5020521 0.07873958 1.816449e-10
## 4 0.3988461 0.32952495 2.275251e-01
## 5 0.5316594 0.20897035 1.168626e-02

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      3BmkaS     MNE7VH outcome exposure                  MR Egger 237.0434
## 2      3BmkaS     MNE7VH outcome exposure Inverse variance weighted 238.1959
##   Q_df     Q_pval
## 1  205 0.06185731
## 2  206 0.06144110
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      3BmkaS     MNE7VH outcome exposure    -0.004414606 0.004421923 0.3192889

Studentized residuals:

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Reference

##         19         45         78         79         99        125        167 
## 0.01880721 0.13144838 0.03711985 0.04752450 0.10103700 0.07282368 0.03294219 
##        181        183        184        186 
## 0.04406035 0.07552836 0.25576172 0.03932365
## [1]  19  45  78  99 183 184 186

Run After deleting new outlier: Final Results:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      3BmkaS     MNE7VH outcome exposure                  MR Egger  180
## 2      3BmkaS     MNE7VH outcome exposure           Weighted median  180
## 3      3BmkaS     MNE7VH outcome exposure Inverse variance weighted  180
## 4      3BmkaS     MNE7VH outcome exposure               Simple mode  180
## 5      3BmkaS     MNE7VH outcome exposure             Weighted mode  180
##           b         se         pval
## 1 0.6174493 0.24939859 1.423045e-02
## 2 0.5034938 0.13046699 1.137743e-04
## 3 0.4361701 0.07962666 4.309154e-08
## 4 0.3931622 0.29682868 1.870115e-01
## 5 0.5046827 0.20982052 1.717767e-02

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      3BmkaS     MNE7VH outcome exposure                  MR Egger 120.7383
## 2      3BmkaS     MNE7VH outcome exposure Inverse variance weighted 121.3266
##   Q_df    Q_pval
## 1  178 0.9996669
## 2  179 0.9996858
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      3BmkaS     MNE7VH outcome exposure    -0.003396271 0.004427943 0.4440924

OR report:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      3BmkaS     MNE7VH outcome exposure                  MR Egger  180
## 2      3BmkaS     MNE7VH outcome exposure           Weighted median  180
## 3      3BmkaS     MNE7VH outcome exposure Inverse variance weighted  180
## 4      3BmkaS     MNE7VH outcome exposure               Simple mode  180
## 5      3BmkaS     MNE7VH outcome exposure             Weighted mode  180
##           b         se         pval      lo_ci     up_ci       or  or_lci95
## 1 0.6174493 0.24939859 1.423045e-02  0.1286280 1.1062705 1.854192 1.1372670
## 2 0.5034938 0.13226360 1.408075e-04  0.2442572 0.7627305 1.654492 1.2766726
## 3 0.4361701 0.07962666 4.309154e-08  0.2801018 0.5922383 1.546772 1.3232646
## 4 0.3931622 0.29260241 1.807546e-01 -0.1803385 0.9666630 1.481659 0.8349875
## 5 0.5046827 0.21261668 1.867135e-02  0.0879540 0.9214114 1.656460 1.0919379
##   or_uci95
## 1 3.023063
## 2 2.144123
## 3 1.808031
## 4 2.629156
## 5 2.512834

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 181 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.437     0.080 0.280, 0.593   0.000
## ------------------------------------------------------------------
## Residual standard error =  0.825 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 122.4505 on 180 degrees of freedom, (p-value = 0.9997). I^2 = 0.0%. 
## F statistic = 53.1.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.428     0.116   0.200 0.656   0.000
##            Weighted median    0.504     0.132   0.245 0.762   0.000
##  Penalized weighted median    0.504     0.132   0.245 0.762   0.000
##                                                                    
##                        IVW    0.437     0.080   0.280 0.593   0.000
##              Penalized IVW    0.437     0.080   0.280 0.593   0.000
##                 Robust IVW    0.436     0.071   0.297 0.574   0.000
##       Penalized robust IVW    0.436     0.071   0.297 0.574   0.000
##                                                                    
##                   MR-Egger    0.617     0.249   0.128 1.106   0.013
##                (intercept)   -0.003     0.004  -0.012 0.005   0.446
##         Penalized MR-Egger    0.617     0.249   0.128 1.106   0.013
##                (intercept)   -0.003     0.004  -0.012 0.005   0.446
##            Robust MR-Egger    0.608     0.135   0.343 0.874   0.000
##                (intercept)   -0.003     0.003  -0.009 0.003   0.272
##  Penalized robust MR-Egger    0.608     0.135   0.343 0.874   0.000
##                (intercept)   -0.003     0.003  -0.009 0.003   0.272

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
3BmkaS MNE7VH exposure outcome 0.0285585 0.0003855 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.4422249
## 
## $beta.se
## [1] 0.08155251
## 
## $beta.p.value
## [1] 5.874535e-08
## 
## $naive.se
## [1] 0.08077311
## 
## $chi.sq.test
## [1] 122.0577
##   over.dispersion loss.function  beta.hat    beta.se
## 1           FALSE            l2 0.4422249 0.08155251
## 2           FALSE         huber 0.4368941 0.08366440
## 3           FALSE         tukey 0.4416286 0.08367047
## 4            TRUE            l2 0.4422247 0.08155846
## 5            TRUE         huber 0.4368941 0.08366994
## 6            TRUE         tukey 0.4416286 0.08367634
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  181 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.442 0.080  0.000 [0.285,0.599]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 181 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.445     0.081 0.286, 0.604   0.000   701.373
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 181 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     MBE    0.521     0.162 0.204, 0.839   0.001
## ------------------------------------------------------------------

HT and BMI

Introduction

  • Title: Investigating the causality between HT on BMI

Data Preparation

1- Number of total SNPs in exposure: 25,494,034 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-5}\):: 14,295 SNPs

3- Number of SNPs exposure after clumping : 179 SNPs

4- Number of total SNPs in outcome: 2,336,260 SNPs

5- Number of common variants between exposure and outcome: 53 SNPs

6- Number of SNPs after harmonization (action=2) = 52 SNPs

7- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 52 SNP

8- Number of SNPs after removing those that have MAF < 0.01 = 52 SNPs

9- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 1 SNPs (rs3184504 was removed)

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   16.55   17.29   18.50   23.50   21.35  199.85

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      6R73uL     oJgXlR outcome exposure                  MR Egger   51
## 2      6R73uL     oJgXlR outcome exposure           Weighted median   51
## 3      6R73uL     oJgXlR outcome exposure Inverse variance weighted   51
## 4      6R73uL     oJgXlR outcome exposure               Simple mode   51
## 5      6R73uL     oJgXlR outcome exposure             Weighted mode   51
##              b          se      pval
## 1  0.005478878 0.010640670 0.6089381
## 2 -0.006486471 0.004935638 0.1887751
## 3  0.002561625 0.004707526 0.5863346
## 4 -0.003191037 0.010075860 0.7527889
## 5 -0.004636483 0.005970222 0.4410524

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      6R73uL     oJgXlR outcome exposure                  MR Egger 134.8623
## 2      6R73uL     oJgXlR outcome exposure Inverse variance weighted 135.1207
##   Q_df       Q_pval
## 1   49 5.943739e-10
## 2   50 9.210749e-10
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      6R73uL     oJgXlR outcome exposure   -0.0003504132 0.001143668 0.7606027

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate          Sd     T-stat
## 1 beta.exposure               Raw     0.002561625 0.004707526  0.5441553
## 2 beta.exposure Outlier-corrected    -0.001297099 0.004051173 -0.3201785
##     P-value
## 1 0.5887531
## 2 0.7502521
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 140.2525
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<1e-04"
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##          RSSobs  Pvalue
## 1  2.176164e-05  0.6324
## 2  3.967156e-05  0.5865
## 3  7.078166e-05       1
## 4  1.823882e-05       1
## 5  2.240769e-07       1
## 6  3.457734e-06       1
## 7  1.357282e-07       1
## 8  2.822947e-07       1
## 9  1.129529e-07       1
## 10 6.675012e-07       1
## 11 1.327403e-06       1
## 12 2.694478e-05       1
## 13 2.555663e-05  0.5049
## 14 2.476527e-05  0.4131
## 15 8.306996e-08       1
## 16 1.057478e-06       1
## 17 1.799852e-07       1
## 18 3.858341e-06       1
## 19 1.398902e-05       1
## 20 2.423330e-05       1
## 21 1.583632e-05       1
## 22 3.281091e-04  0.0051
## 23 3.130348e-06       1
## 24 1.058779e-08       1
## 25 1.470182e-04 <0.0051
## 26 1.340232e-05       1
## 27 3.466707e-05  0.1887
## 28 5.917350e-05       1
## 29 9.684654e-06       1
## 30 1.737656e-06       1
## 31 3.343801e-06       1
## 32 1.207671e-05       1
## 33 9.241574e-06       1
## 34 5.956373e-06       1
## 35 4.444152e-06       1
## 36 5.833958e-06       1
## 37 1.518520e-04       1
## 38 2.978362e-06       1
## 39 2.823519e-07       1
## 40 1.713875e-06       1
## 41 9.829770e-06       1
## 42 4.657619e-07       1
## 43 1.484710e-05       1
## 44 3.482018e-05       1
## 45 5.215603e-05 <0.0051
## 46 3.455497e-07       1
## 47 1.767064e-08       1
## 48 3.328779e-04   0.102
## 49 1.133907e-05       1
## 50 4.964850e-06       1
## 51 1.048428e-06       1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 22 25 45
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##      297.4888 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.1394
##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      6R73uL     oJgXlR outcome exposure                  MR Egger   48
## 2      6R73uL     oJgXlR outcome exposure           Weighted median   48
## 3      6R73uL     oJgXlR outcome exposure Inverse variance weighted   48
## 4      6R73uL     oJgXlR outcome exposure               Simple mode   48
## 5      6R73uL     oJgXlR outcome exposure             Weighted mode   48
##              b          se      pval
## 1  0.003772427 0.009092627 0.6801521
## 2 -0.006518382 0.004899026 0.1833383
## 3 -0.001297099 0.004051173 0.7488330
## 4 -0.002995373 0.010321049 0.7729247
## 5 -0.005015259 0.005798345 0.3914614

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      6R73uL     oJgXlR outcome exposure                  MR Egger 89.61718
## 2      6R73uL     oJgXlR outcome exposure Inverse variance weighted 90.37526
##   Q_df       Q_pval
## 1   46 0.0001249282
## 2   47 0.0001468992
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      6R73uL     oJgXlR outcome exposure   -0.0006114995 0.0009802972
##        pval
## 1 0.5358468

Radial test

## 
## Radial IVW
## 
##                      Estimate   Std.Error    t value  Pr(>|t|)
## Effect (Mod.2nd) -0.001297311 0.004051304 -0.3202205 0.7488012
## Iterative        -0.001297311 0.004051304 -0.3202205 0.7488012
## Exact (FE)       -0.001406333 0.002921940 -0.4813012 0.6303025
## Exact (RE)       -0.001368682 0.004215002 -0.3247168 0.7468364
## 
## 
## Residual standard error: 1.387 on 47 degrees of freedom
## 
## F-statistic: 0.1 on 1 and 47 DF, p-value: 0.75
## Q-Statistic for heterogeneity: 90.35764 on 47 DF , p-value: 0.000147575
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"

Studentized residuals:

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Reference

##        26        35        45 
## 0.3483251 0.4241893 2.4966278
## [1]  3 35 45

Run After deleting new outlier: Final Results:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      6R73uL     oJgXlR outcome exposure                  MR Egger   36
## 2      6R73uL     oJgXlR outcome exposure           Weighted median   36
## 3      6R73uL     oJgXlR outcome exposure Inverse variance weighted   36
## 4      6R73uL     oJgXlR outcome exposure               Simple mode   36
## 5      6R73uL     oJgXlR outcome exposure             Weighted mode   36
##              b          se       pval
## 1 -0.006751707 0.012084552 0.58002401
## 2 -0.007676646 0.005608408 0.17106977
## 3 -0.008930918 0.003691611 0.01555269
## 4 -0.002309960 0.009986617 0.81842434
## 5 -0.005702722 0.008029400 0.48226719

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      6R73uL     oJgXlR outcome exposure                  MR Egger 36.48178
## 2      6R73uL     oJgXlR outcome exposure Inverse variance weighted 36.52037
##   Q_df    Q_pval
## 1   34 0.3540488
## 2   35 0.3979494
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      6R73uL     oJgXlR outcome exposure    -0.000214724 0.001132153 0.8507034

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 36 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI        p-value
##     IVW   -0.009     0.004 -0.016, -0.002   0.016
## ------------------------------------------------------------------
## Residual standard error =  1.021 
## Heterogeneity test statistic (Cochran's Q) = 36.5204 on 35 degrees of freedom, (p-value = 0.3979). I^2 = 4.2%. 
## F statistic = 20.3.
##                     Method Estimate Std Error 95% CI         P-value
##              Simple median   -0.007     0.005  -0.017  0.004   0.193
##            Weighted median   -0.008     0.006  -0.019  0.004   0.177
##  Penalized weighted median   -0.008     0.006  -0.019  0.004   0.183
##                                                                     
##                        IVW   -0.009     0.004  -0.016 -0.002   0.016
##              Penalized IVW   -0.009     0.004  -0.016 -0.002   0.016
##                 Robust IVW   -0.008     0.003  -0.015 -0.001   0.017
##       Penalized robust IVW   -0.008     0.003  -0.015 -0.001   0.017
##                                                                     
##                   MR-Egger   -0.007     0.012  -0.030  0.017   0.576
##                (intercept)    0.000     0.001  -0.002  0.002   0.850
##         Penalized MR-Egger   -0.007     0.012  -0.030  0.017   0.576
##                (intercept)    0.000     0.001  -0.002  0.002   0.850
##            Robust MR-Egger   -0.005     0.007  -0.019  0.008   0.429
##                (intercept)    0.000     0.001  -0.002  0.001   0.702
##  Penalized robust MR-Egger   -0.005     0.007  -0.019  0.008   0.429
##                (intercept)    0.000     0.001  -0.002  0.001   0.702

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
6R73uL oJgXlR exposure outcome 0.0018481 9.34e-05 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] -0.009356963
## 
## $beta.se
## [1] 0.003839895
## 
## $beta.p.value
## [1] 0.01481886
## 
## $naive.se
## [1] 0.003743696
## 
## $chi.sq.test
## [1] 36.23195
##   over.dispersion loss.function     beta.hat     beta.se
## 1           FALSE            l2 -0.009356963 0.003839895
## 2           FALSE         huber -0.008720771 0.003932553
## 3           FALSE         tukey -0.008645906 0.003931756
## 4            TRUE            l2 -0.009355925 0.003845568
## 5            TRUE         huber -0.008712942 0.003935069
## 6            TRUE         tukey -0.008647392 0.003934428
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  36 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue          95% CI
##  cML-MA-BIC   -0.009 0.004  0.013 [-0.017,-0.002]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 36 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI        p-value Condition
##    dIVW   -0.009     0.004 -0.017, -0.002   0.014   115.867
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 36 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE   -0.006     0.007 -0.020, 0.009   0.433
## ------------------------------------------------------------------

HT and WHR

Introduction

Data Preparation

1- Number of total SNPs in exposure: 25,494,034 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-5}\): 14,295 SNPs

3- Number of SNPs exposure after clumping : 179 SNPs

4- Number of total SNPs in outcome: 2,560,781 SNPs

5- Number of common variants between exposure and outcome: 58 SNPs

6- Number of SNPs after harmonization (action=2) = 57 SNPs

7- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 57 SNP

8- Number of SNPs after removing those that have MAF < 0.01 = 57 SNPs

9- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   16.55   17.29   18.65   24.76   22.23  199.85

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      6R73uL     so70k9 outcome exposure                  MR Egger   57
## 2      6R73uL     so70k9 outcome exposure           Weighted median   57
## 3      6R73uL     so70k9 outcome exposure Inverse variance weighted   57
## 4      6R73uL     so70k9 outcome exposure               Simple mode   57
## 5      6R73uL     so70k9 outcome exposure             Weighted mode   57
##              b          se      pval
## 1  0.006727232 0.014697405 0.6489599
## 2 -0.003899528 0.009693418 0.6874734
## 3 -0.001203778 0.006551602 0.8542191
## 4  0.011411625 0.018440798 0.5385409
## 5 -0.003863494 0.010958315 0.7257398

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      6R73uL     so70k9 outcome exposure                  MR Egger 61.58845
## 2      6R73uL     so70k9 outcome exposure Inverse variance weighted 61.99655
##   Q_df    Q_pval
## 1   55 0.2521533
## 2   56 0.2709054
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      6R73uL     so70k9 outcome exposure   -0.0009761701 0.001617016 0.5485341

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate          Sd     T-stat
## 1 beta.exposure               Raw    -0.001203778 0.006551602 -0.1837379
## 2 beta.exposure Outlier-corrected              NA          NA         NA
##     P-value
## 1 0.8548827
## 2        NA
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 63.93178
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.3

Studentized residuals:

Radial test

## 
## Radial IVW
## 
##                      Estimate   Std.Error    t value  Pr(>|t|)
## Effect (Mod.2nd) -0.001203861 0.006551651 -0.1837492 0.8542102
## Iterative        -0.001203861 0.006551651 -0.1837492 0.8542102
## Exact (FE)       -0.001254362 0.006226827 -0.2014448 0.8403508
## Exact (RE)       -0.001265589 0.006854806 -0.1846280 0.8541878
## 
## 
## Residual standard error: 1.052 on 56 degrees of freedom
## 
## F-statistic: 0.03 on 1 and 56 DF, p-value: 0.855
## Q-Statistic for heterogeneity: 61.9951 on 56 DF , p-value: 0.2709476
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Reference

##          5         12         39         46 
## 0.07693315 0.10001636 0.12225943 0.14141363
## [1]  5 23 28 46 52

Run After deleting new outlier: Final Results:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      6R73uL     so70k9 outcome exposure                  MR Egger   39
## 2      6R73uL     so70k9 outcome exposure           Weighted median   39
## 3      6R73uL     so70k9 outcome exposure Inverse variance weighted   39
## 4      6R73uL     so70k9 outcome exposure               Simple mode   39
## 5      6R73uL     so70k9 outcome exposure             Weighted mode   39
##            b          se       pval
## 1 0.01447472 0.019861103 0.47071360
## 2 0.01370317 0.012039403 0.25503985
## 3 0.01818502 0.008278459 0.02804421
## 4 0.01947715 0.021896753 0.37933133
## 5 0.01375097 0.016154081 0.39996963

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      6R73uL     so70k9 outcome exposure                  MR Egger 13.59590
## 2      6R73uL     so70k9 outcome exposure Inverse variance weighted 13.63813
##   Q_df    Q_pval
## 1   37 0.9998470
## 2   38 0.9999066
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      6R73uL     so70k9 outcome exposure    0.0004219058 0.002052908 0.8382954

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 39 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.018     0.008 0.002, 0.034   0.028
## ------------------------------------------------------------------
## Residual standard error =  0.599 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 13.6381 on 38 degrees of freedom, (p-value = 0.9999). I^2 = 0.0%. 
## F statistic = 20.3.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.022     0.012  -0.001 0.045   0.065
##            Weighted median    0.015     0.012  -0.009 0.039   0.222
##  Penalized weighted median    0.015     0.012  -0.009 0.039   0.222
##                                                                    
##                        IVW    0.018     0.008   0.002 0.034   0.028
##              Penalized IVW    0.018     0.008   0.002 0.034   0.028
##                 Robust IVW    0.018     0.008   0.002 0.035   0.027
##       Penalized robust IVW    0.018     0.008   0.002 0.035   0.027
##                                                                    
##                   MR-Egger    0.014     0.020  -0.024 0.053   0.466
##                (intercept)    0.000     0.002  -0.004 0.004   0.837
##         Penalized MR-Egger    0.014     0.020  -0.024 0.053   0.466
##                (intercept)    0.000     0.002  -0.004 0.004   0.837
##            Robust MR-Egger    0.017     0.022  -0.026 0.061   0.438
##                (intercept)    0.000     0.002  -0.004 0.004   0.951
##  Penalized robust MR-Egger    0.017     0.022  -0.026 0.061   0.438
##                (intercept)    0.000     0.002  -0.004 0.004   0.951

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
6R73uL so70k9 exposure outcome 0.0020064 0.0001279 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.01857792
## 
## $beta.se
## [1] 0.008931523
## 
## $beta.p.value
## [1] 0.03752191
## 
## $naive.se
## [1] 0.008703363
## 
## $chi.sq.test
## [1] 13.54942
##   over.dispersion loss.function   beta.hat     beta.se
## 1           FALSE            l2 0.01857792 0.008931523
## 2           FALSE         huber 0.01883015 0.009166148
## 3           FALSE         tukey 0.01867057 0.009164514
## 4            TRUE            l2 0.01857807 0.008937414
## 5            TRUE         huber 0.01883031 0.009171609
## 6            TRUE         tukey 0.01867156 0.009170091
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  39 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.019 0.008  0.028 [0.002,0.035]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 39 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.019     0.009 0.002, 0.036   0.029   120.766
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 39 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.014     0.013 -0.013, 0.040   0.305
## ------------------------------------------------------------------

HT and BFP

Introduction

  • Title: Investigating the causality between HT on BFP

Data Preparation

1- Number of total SNPs in exposure: 25,494,034 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-5}\): 14,295 SNPs

3- Number of SNPs exposure after clumping : 179 SNPs

4- Number of total SNPs in outcome: 9,837,128 SNPs

5- Number of common variants between exposure and outcome: 174 SNPs

6- Number of SNPs after harmonization (action=2) = 171 SNPs

7- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 170 SNP

8- Number of SNPs after removing those that have MAF < 0.01 = 170 SNPs

9- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   16.46   17.35   18.50   23.55   20.83  199.85

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      6R73uL     H7ku4J outcome exposure                  MR Egger  170
## 2      6R73uL     H7ku4J outcome exposure           Weighted median  170
## 3      6R73uL     H7ku4J outcome exposure Inverse variance weighted  170
## 4      6R73uL     H7ku4J outcome exposure               Simple mode  170
## 5      6R73uL     H7ku4J outcome exposure             Weighted mode  170
##               b          se      pval
## 1 -0.0013975025 0.002596241 0.5910967
## 2  0.0013232251 0.002024215 0.5133066
## 3 -0.0009193387 0.001705339 0.5898216
## 4  0.0029282555 0.004129605 0.4792466
## 5  0.0020707490 0.001720001 0.2303027

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      6R73uL     H7ku4J outcome exposure                  MR Egger 415.1483
## 2      6R73uL     H7ku4J outcome exposure Inverse variance weighted 415.2963
##   Q_df       Q_pval
## 1  168 6.316287e-23
## 2  169 9.548802e-23
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      6R73uL     H7ku4J outcome exposure    9.889651e-05 0.0004040262
##        pval
## 1 0.8069275

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate          Sd     T-stat
## 1 beta.exposure               Raw   -0.0009193387 0.001705339 -0.5390945
## 2 beta.exposure Outlier-corrected    0.0004747984 0.001557938  0.3047607
##     P-value
## 1 0.5905311
## 2 0.7609348
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 420.1567
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<5e-05"
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##           RSSobs  Pvalue
## 1   2.993968e-06       1
## 2   3.223111e-05       1
## 3   4.002378e-05       1
## 4   1.722641e-09       1
## 5   9.302219e-08       1
## 6   6.915705e-06       1
## 7   5.104750e-07       1
## 8   2.665580e-05   0.918
## 9   4.663404e-05       1
## 10  2.541573e-06       1
## 11  1.376828e-06       1
## 12  1.710315e-06       1
## 13  1.223640e-05       1
## 14  6.941038e-06       1
## 15  1.342163e-06       1
## 16  7.348622e-06       1
## 17  4.859750e-05       1
## 18  7.057936e-05       1
## 19  1.615943e-10       1
## 20  2.903026e-07       1
## 21  8.853423e-08       1
## 22  9.228169e-07       1
## 23  1.436251e-05       1
## 24  8.371351e-05       1
## 25  7.019588e-05  0.6715
## 26  1.651028e-05       1
## 27  9.712558e-06       1
## 28  1.230300e-05       1
## 29  6.773404e-06       1
## 30  3.987884e-05       1
## 31  1.481176e-06       1
## 32  7.336443e-07       1
## 33  1.276333e-05       1
## 34  2.730236e-04       1
## 35  2.402538e-06       1
## 36  3.103574e-07       1
## 37  2.722363e-05  0.1445
## 38  1.871629e-07       1
## 39  5.615570e-07       1
## 40  2.559324e-06       1
## 41  4.579748e-07       1
## 42  4.896427e-06       1
## 43  1.700648e-07       1
## 44  4.679496e-06       1
## 45  3.442357e-06       1
## 46  2.374991e-05  0.6715
## 48  2.440696e-07       1
## 49  1.599876e-05       1
## 50  3.627748e-06       1
## 51  2.308251e-05       1
## 52  2.430817e-05       1
## 53  2.530929e-06       1
## 54  1.893233e-04       1
## 55  2.677875e-05       1
## 56  1.077165e-04       1
## 57  4.767320e-06       1
## 58  4.291139e-05       1
## 59  2.795432e-05       1
## 60  3.750534e-06       1
## 61  6.889389e-06       1
## 62  3.930673e-05       1
## 63  5.472017e-05       1
## 64  1.147280e-04       1
## 65  8.763319e-05       1
## 66  4.318159e-05       1
## 67  4.474650e-07       1
## 68  5.076759e-07       1
## 69  1.406887e-05       1
## 70  1.710061e-06       1
## 71  2.117642e-05       1
## 72  1.796520e-06       1
## 73  3.285509e-05   0.119
## 74  6.133388e-06       1
## 75  9.724229e-05       1
## 76  1.247020e-04       1
## 77  5.149732e-06       1
## 78  2.477891e-08       1
## 79  4.648037e-05   0.102
## 80  2.151342e-07       1
## 81  1.604179e-05       1
## 82  4.213302e-05       1
## 83  1.594964e-07       1
## 84  1.195735e-05       1
## 85  2.422739e-07       1
## 86  6.625862e-06       1
## 87  3.836948e-07       1
## 88  2.007719e-05   0.629
## 89  1.817835e-07       1
## 90  1.993733e-07       1
## 91  1.369355e-05       1
## 92  1.486756e-05       1
## 93  7.355240e-08       1
## 94  2.431221e-05       1
## 95  4.401070e-07       1
## 96  7.760977e-06       1
## 97  2.111315e-05  0.5355
## 98  4.744243e-07       1
## 99  1.638029e-07       1
## 100 6.261488e-05       1
## 101 6.225098e-06       1
## 102 5.075939e-08       1
## 103 4.134598e-05       1
## 104 4.424728e-05       1
## 105 3.384630e-09       1
## 106 2.135825e-06       1
## 107 1.060340e-05       1
## 108 2.578466e-06       1
## 109 4.789620e-09       1
## 110 1.582819e-05       1
## 111 3.536323e-06       1
## 112 4.816191e-06       1
## 113 9.664179e-07       1
## 114 2.962571e-07       1
## 115 6.132967e-06       1
## 116 1.787221e-06       1
## 117 2.249929e-05       1
## 118 9.334738e-08       1
## 119 3.537698e-04 <0.0085
## 120 5.553294e-06       1
## 121 4.405861e-06       1
## 122 5.647194e-05       1
## 123 1.047782e-05       1
## 124 7.769589e-07       1
## 125 1.195450e-05       1
## 126 3.759240e-07       1
## 127 3.685785e-05    0.68
## 128 4.821198e-06       1
## 129 1.302976e-06       1
## 130 4.494270e-06       1
## 131 3.194921e-08       1
## 132 8.968590e-07       1
## 133 2.283821e-05       1
## 134 1.991849e-06       1
## 135 2.469714e-06       1
## 136 3.156653e-08       1
## 137 1.506738e-07       1
## 138 2.405914e-05       1
## 139 1.496503e-05       1
## 140 5.775510e-06       1
## 141 6.396838e-07       1
## 142 5.081249e-05       1
## 143 9.795254e-06       1
## 144 2.756790e-06       1
## 145 1.581839e-04       1
## 146 3.943027e-06       1
## 147 1.260562e-04       1
## 148 2.520379e-06       1
## 149 4.369437e-04 <0.0085
## 150 7.267053e-05  0.3485
## 151 7.946165e-05   0.068
## 152 1.558277e-04 <0.0085
## 153 4.910289e-06       1
## 154 8.791249e-07       1
## 155 6.746693e-07       1
## 156 2.182593e-06       1
## 157 1.182095e-05       1
## 158 2.698137e-04       1
## 159 8.379539e-06       1
## 160 1.929714e-04 <0.0085
## 161 1.467221e-06       1
## 162 2.931246e-05       1
## 163 1.104821e-06       1
## 164 3.581255e-07       1
## 165 6.750336e-06       1
## 166 4.416109e-05 <0.0085
## 167 2.209820e-06       1
## 168 6.475971e-06       1
## 169 3.994662e-07       1
## 170 4.861213e-06       1
## 171 3.136828e-07       1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 118 148 151 159 165
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##     -293.6272 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.15685
##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      6R73uL     H7ku4J outcome exposure                  MR Egger  165
## 2      6R73uL     H7ku4J outcome exposure           Weighted median  165
## 3      6R73uL     H7ku4J outcome exposure Inverse variance weighted  165
## 4      6R73uL     H7ku4J outcome exposure               Simple mode  165
## 5      6R73uL     H7ku4J outcome exposure             Weighted mode  165
##              b          se      pval
## 1 0.0001946182 0.002350816 0.9341221
## 2 0.0013464596 0.001943286 0.4883863
## 3 0.0004747984 0.001557938 0.7605484
## 4 0.0032381756 0.004064939 0.4268287
## 5 0.0019749158 0.001729258 0.2550938

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      6R73uL     H7ku4J outcome exposure                  MR Egger 319.9986
## 2      6R73uL     H7ku4J outcome exposure Inverse variance weighted 320.0485
##   Q_df       Q_pval
## 1  163 2.722104e-12
## 2  164 3.795524e-12
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      6R73uL     H7ku4J outcome exposure    5.752233e-05 0.0003605807
##        pval
## 1 0.8734512

Radial test

## 
## Radial IVW
## 
##                      Estimate   Std.Error   t value  Pr(>|t|)
## Effect (Mod.2nd) 0.0004742166 0.001558239 0.3043284 0.7608777
## Iterative        0.0004742166 0.001558239 0.3043284 0.7608777
## Exact (FE)       0.0004894686 0.001115481 0.4387962 0.6608092
## Exact (RE)       0.0004846189 0.001418492 0.3416437 0.7330564
## 
## 
## Residual standard error: 1.397 on 164 degrees of freedom
## 
## F-statistic: 0.09 on 1 and 164 DF, p-value: 0.761
## Q-Statistic for heterogeneity: 320.0367 on 164 DF , p-value: 3.806746e-12
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"

Studentized residuals:

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Reference

##  [1]  24  34  53  55  64  74  75 143 145 154

Run After deleting new outlier: Final Results:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      6R73uL     H7ku4J outcome exposure                  MR Egger  134
## 2      6R73uL     H7ku4J outcome exposure           Weighted median  134
## 3      6R73uL     H7ku4J outcome exposure Inverse variance weighted  134
## 4      6R73uL     H7ku4J outcome exposure               Simple mode  134
## 5      6R73uL     H7ku4J outcome exposure             Weighted mode  134
##             b          se       pval
## 1 0.001418850 0.001848012 0.44399428
## 2 0.002254136 0.001923568 0.24125657
## 3 0.003045252 0.001258795 0.01555548
## 4 0.003730695 0.004271566 0.38403078
## 5 0.001754246 0.001741085 0.31549596

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      6R73uL     H7ku4J outcome exposure                  MR Egger 152.8676
## 2      6R73uL     H7ku4J outcome exposure Inverse variance weighted 154.5363
##   Q_df     Q_pval
## 1  132 0.10333141
## 2  133 0.09755242
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      6R73uL     H7ku4J outcome exposure    0.0003421534 0.0002850413
##        pval
## 1 0.2321476

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 134 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.003     0.001 0.001, 0.006   0.016
## ------------------------------------------------------------------
## Residual standard error =  1.078 
## Heterogeneity test statistic (Cochran's Q) = 154.5363 on 133 degrees of freedom, (p-value = 0.0976). I^2 = 13.9%. 
## F statistic = 23.5.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.003     0.002  -0.001 0.007   0.134
##            Weighted median    0.002     0.002  -0.001 0.006   0.232
##  Penalized weighted median    0.002     0.002  -0.002 0.006   0.347
##                                                                    
##                        IVW    0.003     0.001   0.001 0.006   0.016
##              Penalized IVW    0.003     0.001   0.000 0.005   0.024
##                 Robust IVW    0.002     0.001   0.000 0.004   0.044
##       Penalized robust IVW    0.002     0.001   0.000 0.004   0.042
##                                                                    
##                   MR-Egger    0.001     0.002  -0.002 0.005   0.443
##                (intercept)    0.000     0.000   0.000 0.001   0.230
##         Penalized MR-Egger    0.002     0.002  -0.002 0.005   0.367
##                (intercept)    0.000     0.000   0.000 0.001   0.341
##            Robust MR-Egger    0.002     0.001   0.000 0.004   0.139
##                (intercept)    0.000     0.000   0.000 0.001   0.631
##  Penalized robust MR-Egger    0.002     0.001   0.000 0.004   0.130
##                (intercept)    0.000     0.000   0.000 0.001   0.642

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
6R73uL H7ku4J exposure outcome 0.0079555 0.0003548 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.003206916
## 
## $beta.se
## [1] 0.001250331
## 
## $beta.p.value
## [1] 0.01032194
## 
## $naive.se
## [1] 0.001219894
## 
## $chi.sq.test
## [1] 154.2275
##   over.dispersion loss.function    beta.hat     beta.se
## 1           FALSE            l2 0.003206916 0.001250331
## 2           FALSE         huber 0.002206292 0.001270191
## 3           FALSE         tukey 0.002253920 0.001270698
## 4            TRUE            l2 0.003204189 0.001252717
## 5            TRUE         huber 0.002212728 0.001270962
## 6            TRUE         tukey 0.002261531 0.001271542
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  134 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.003 0.001  0.010 [0.001,0.006]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 134 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.003     0.001 0.001, 0.006   0.015   260.463
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 134 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.002     0.002 -0.002, 0.005   0.302
## ------------------------------------------------------------------

HT and WC

Introduction

  • Title: Investigating the causality between HT on WC

Data Preparation

1- Number of total SNPs in exposure: 25,494,034 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-5}\): 14,295 SNPs

3- Number of SNPs exposure after clumping : 179 SNPs

4- Number of total SNPs in outcome: 10,545,186 SNPs

5- Number of common variants between exposure and outcome: 168 SNPs

6- Number of SNPs after harmonization (action=2) = 165 SNPs

7- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 162 SNP

8- Number of SNPs after removing those that have MAF < 0.01 = 162 SNPs

9- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 1 SNPs (rs76121445 was removed)

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   16.46   17.39   18.51   23.71   20.86  199.85

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      6R73uL     7BHc6A outcome exposure                  MR Egger  161
## 2      6R73uL     7BHc6A outcome exposure           Weighted median  161
## 3      6R73uL     7BHc6A outcome exposure Inverse variance weighted  161
## 4      6R73uL     7BHc6A outcome exposure               Simple mode  161
## 5      6R73uL     7BHc6A outcome exposure             Weighted mode  161
##              b          se      pval
## 1 -0.002210156 0.003312126 0.5055528
## 2 -0.001641161 0.003114782 0.5982670
## 3  0.003327312 0.002221375 0.1341692
## 4 -0.001873353 0.007171434 0.7942554
## 5 -0.002424260 0.002569686 0.3468952

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      6R73uL     7BHc6A outcome exposure                  MR Egger 318.3255
## 2      6R73uL     7BHc6A outcome exposure Inverse variance weighted 328.2986
##   Q_df       Q_pval
## 1  159 1.021194e-12
## 2  160 1.105737e-13
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      6R73uL     7BHc6A outcome exposure     0.001140525 0.0005110046
##         pval
## 1 0.02701746

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate          Sd   T-stat
## 1 beta.exposure               Raw     0.003327312 0.002221375 1.497862
## 2 beta.exposure Outlier-corrected     0.003351006 0.002154507 1.555347
##     P-value
## 1 0.1361394
## 2 0.1218642
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 333.0604
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<4e-05"
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##           RSSobs  Pvalue
## 1   1.083801e-06       1
## 2   3.523556e-05       1
## 3   1.303273e-04       1
## 4   1.063530e-06       1
## 5   3.080596e-06       1
## 6   4.148264e-06       1
## 7   8.715192e-07       1
## 8   2.413899e-05       1
## 9   7.620106e-05       1
## 10  1.059277e-06       1
## 11  3.741748e-07       1
## 12  2.138889e-05       1
## 13  1.947290e-05       1
## 14  5.833383e-06       1
## 15  6.555700e-06       1
## 16  2.518988e-06       1
## 17  1.782016e-04       1
## 18  9.742534e-04       1
## 19  3.667826e-08       1
## 20  2.175583e-05       1
## 21  1.663309e-05       1
## 22  4.556503e-08       1
## 23  8.023767e-06       1
## 24  9.767583e-05       1
## 25  6.803576e-05       1
## 26  1.152534e-09       1
## 27  2.366667e-05       1
## 28  4.570747e-05  0.3542
## 29  1.427864e-05       1
## 30  1.242892e-05       1
## 31  2.991978e-06       1
## 32  4.213713e-08       1
## 33  3.284766e-05       1
## 34  3.615531e-04       1
## 35  1.519815e-07       1
## 36  1.921884e-07       1
## 37  2.337238e-05       1
## 38  8.845814e-06       1
## 39  4.886524e-06       1
## 40  1.735210e-05       1
## 41  1.977244e-05       1
## 42  7.547959e-06       1
## 43  1.408294e-08       1
## 44  1.512739e-07       1
## 45  9.015672e-06       1
## 46  2.459540e-05       1
## 48  1.249408e-06       1
## 49  4.020778e-06       1
## 50  1.244066e-07       1
## 51  2.035851e-05       1
## 52  1.937992e-03       1
## 53  3.288365e-06       1
## 54  6.768536e-06       1
## 55  1.525007e-04       1
## 56  1.095689e-05       1
## 57  8.440530e-07       1
## 58  1.687917e-06       1
## 59  1.664257e-04       1
## 60  2.353381e-04       1
## 61  1.508197e-04       1
## 62  1.581029e-04       1
## 63  7.082876e-04       1
## 64  3.011190e-06       1
## 65  9.747415e-07       1
## 66  2.793201e-05       1
## 67  8.775126e-07       1
## 68  3.306591e-06       1
## 69  3.114949e-05       1
## 70  1.306202e-05       1
## 71  2.440744e-06       1
## 72  5.583718e-05 0.25116
## 73  1.549755e-05       1
## 74  9.014785e-04 0.09016
## 75  2.185922e-04       1
## 76  9.623372e-05       1
## 77  1.708361e-07       1
## 78  6.796791e-05 0.43148
## 79  7.883293e-07       1
## 80  6.376698e-06       1
## 81  1.875865e-04 0.13524
## 82  4.627589e-10       1
## 83  1.050435e-05       1
## 84  5.660097e-09       1
## 85  6.191976e-08       1
## 86  1.238448e-05       1
## 87  6.628403e-07       1
## 88  3.223876e-06       1
## 89  2.535464e-06       1
## 90  5.273577e-05       1
## 91  4.210885e-08       1
## 92  1.609539e-05       1
## 93  3.399226e-07       1
## 94  2.918507e-06       1
## 95  5.819685e-07       1
## 96  1.932479e-05       1
## 97  2.724513e-06       1
## 98  5.380784e-10       1
## 99  3.490462e-04       1
## 100 1.927300e-06       1
## 101 3.924309e-05 0.40572
## 102 1.480927e-05       1
## 103 4.093293e-05       1
## 104 9.851894e-06       1
## 105 1.370135e-05       1
## 106 5.741842e-05       1
## 107 4.276537e-06       1
## 108 8.245868e-07       1
## 109 6.940826e-05       1
## 110 6.579292e-06       1
## 111 2.411837e-08       1
## 112 2.014650e-06       1
## 113 8.704087e-07       1
## 114 1.896175e-07       1
## 115 2.566534e-05       1
## 116 3.934184e-06       1
## 117 3.997442e-04  0.0322
## 118 1.483805e-05       1
## 119 3.029389e-06       1
## 120 4.599248e-07       1
## 121 2.910009e-05       1
## 122 1.745002e-04 0.32844
## 123 5.265811e-05       1
## 124 2.380212e-05       1
## 125 2.213171e-05       1
## 126 5.082176e-06       1
## 127 8.652006e-05       1
## 128 1.042280e-05       1
## 129 3.566747e-06       1
## 130 1.971190e-06       1
## 131 2.348087e-05       1
## 132 1.368100e-05       1
## 133 5.230015e-06       1
## 134 6.155218e-08       1
## 136 3.643073e-05       1
## 137 2.939079e-05       1
## 138 4.982820e-09       1
## 139 6.849058e-05       1
## 140 3.937192e-06       1
## 141 5.189563e-06       1
## 142 1.952222e-04       1
## 143 3.640331e-07       1
## 144 2.039154e-04       1
## 145 2.868000e-05       1
## 146 9.655415e-05       1
## 147 8.247561e-05       1
## 149 6.241155e-06       1
## 150 3.860011e-06       1
## 151 4.063901e-05       1
## 152 8.231531e-07       1
## 153 3.345050e-05       1
## 154 2.089742e-04       1
## 155 2.878644e-04 0.04508
## 156 5.586490e-06       1
## 157 2.411955e-05       1
## 158 3.293509e-08       1
## 159 1.467490e-05       1
## 160 8.829188e-06       1
## 162 9.302383e-05       1
## 163 8.149381e-07       1
## 164 6.747971e-06       1
## 165 7.936025e-07       1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 116 152
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##    -0.7070675 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.99132
##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      6R73uL     7BHc6A outcome exposure                  MR Egger  159
## 2      6R73uL     7BHc6A outcome exposure           Weighted median  159
## 3      6R73uL     7BHc6A outcome exposure Inverse variance weighted  159
## 4      6R73uL     7BHc6A outcome exposure               Simple mode  159
## 5      6R73uL     7BHc6A outcome exposure             Weighted mode  159
##              b          se      pval
## 1 -0.002021410 0.003198106 0.5282640
## 2 -0.001641042 0.003157126 0.6032101
## 3  0.003491301 0.002150272 0.1044493
## 4 -0.001673982 0.007545969 0.8247266
## 5 -0.002177075 0.002583624 0.4007013

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      6R73uL     7BHc6A outcome exposure                  MR Egger 291.9129
## 2      6R73uL     7BHc6A outcome exposure Inverse variance weighted 301.7794
##   Q_df       Q_pval
## 1  157 3.581292e-10
## 2  158 4.579940e-11
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      6R73uL     7BHc6A outcome exposure     0.001134486 0.0004924854
##         pval
## 1 0.02255727

Radial test

## 
## Radial IVW
## 
##                     Estimate   Std.Error  t value   Pr(>|t|)
## Effect (Mod.2nd) 0.003553541 0.002160589 1.644710 0.10002971
## Iterative        0.003553541 0.002160589 1.644710 0.10002971
## Exact (FE)       0.003952520 0.001566989 2.522366 0.01165682
## Exact (RE)       0.003707247 0.002651300 1.398275 0.16399018
## 
## 
## Residual standard error: 1.381 on 158 degrees of freedom
## 
## F-statistic: 2.71 on 1 and 158 DF, p-value: 0.102
## Q-Statistic for heterogeneity: 301.2983 on 158 DF , p-value: 5.152118e-11
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"

Studentized residuals:

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Reference

Run After deleting new outlier: Final Results:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      6R73uL     7BHc6A outcome exposure                  MR Egger  125
## 2      6R73uL     7BHc6A outcome exposure           Weighted median  125
## 3      6R73uL     7BHc6A outcome exposure Inverse variance weighted  125
## 4      6R73uL     7BHc6A outcome exposure               Simple mode  125
## 5      6R73uL     7BHc6A outcome exposure             Weighted mode  125
##               b          se         pval
## 1  1.183682e-02 0.005196701 2.446742e-02
## 2  6.700444e-03 0.003958383 9.050826e-02
## 3  1.312719e-02 0.002407227 4.945930e-08
## 4 -3.720637e-06 0.010190699 9.997093e-01
## 5  3.059193e-03 0.007136228 6.688964e-01

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      6R73uL     7BHc6A outcome exposure                  MR Egger 121.1337
## 2      6R73uL     7BHc6A outcome exposure Inverse variance weighted 121.2122
##   Q_df    Q_pval
## 1  123 0.5306974
## 2  124 0.5540659
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      6R73uL     7BHc6A outcome exposure    0.0001626082 0.0005803708
##        pval
## 1 0.7798101

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 125 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.013     0.002 0.008, 0.018   0.000
## ------------------------------------------------------------------
## Residual standard error =  0.989 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 121.2122 on 124 degrees of freedom, (p-value = 0.5541). I^2 = 0.0%. 
## F statistic = 20.1.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.007     0.004   0.000 0.014   0.065
##            Weighted median    0.009     0.004   0.001 0.017   0.033
##  Penalized weighted median    0.008     0.004   0.000 0.016   0.039
##                                                                    
##                        IVW    0.013     0.002   0.008 0.018   0.000
##              Penalized IVW    0.013     0.002   0.008 0.018   0.000
##                 Robust IVW    0.012     0.003   0.007 0.017   0.000
##       Penalized robust IVW    0.012     0.003   0.007 0.017   0.000
##                                                                    
##                   MR-Egger    0.012     0.005   0.002 0.022   0.023
##                (intercept)    0.000     0.001  -0.001 0.001   0.779
##         Penalized MR-Egger    0.012     0.005   0.002 0.022   0.023
##                (intercept)    0.000     0.001  -0.001 0.001   0.779
##            Robust MR-Egger    0.011     0.005   0.001 0.021   0.034
##                (intercept)    0.000     0.001  -0.001 0.001   0.776
##  Penalized robust MR-Egger    0.011     0.005   0.001 0.021   0.034
##                (intercept)    0.000     0.001  -0.001 0.001   0.776

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
6R73uL 7BHc6A exposure outcome 0.0063675 0.0004484 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.01379663
## 
## $beta.se
## [1] 0.00256772
## 
## $beta.p.value
## [1] 7.739192e-08
## 
## $naive.se
## [1] 0.002503808
## 
## $chi.sq.test
## [1] 119.7756
##   over.dispersion loss.function   beta.hat     beta.se
## 1           FALSE            l2 0.01379663 0.002567720
## 2           FALSE         huber 0.01308101 0.002629427
## 3           FALSE         tukey 0.01294610 0.002628516
## 4            TRUE            l2 0.01379606 0.002571626
## 5            TRUE         huber 0.01310340 0.002673050
## 6            TRUE         tukey 0.01295295 0.002662056
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  125 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.014 0.003  0.000 [0.009,0.019]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 125 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.014     0.003 0.009, 0.019   0.000   214.094
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 125 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.003     0.007 -0.011, 0.017   0.662
## ------------------------------------------------------------------

Multivariable MR

Checking weakness of the instruments:

## 
## Conditional F-statistics for instrument strength
## 
##             exposure1 exposure2 exposure3
## F-statistic  62.89468  42.04917  70.12359

How many SNPs have been eliminated with checking the weakness: 0 SNP

initial IVW-MVMR:

## 
## Multivariable MR
## 
##             Estimate Std. Error   t value   Pr(>|t|)
## exposure1 0.17763275  0.1899744 0.9350351 0.36039864
## exposure2 0.08922646  0.1919340 0.4648810 0.64680086
## exposure3 0.45932468  0.2084595 2.2034241 0.03886521
## 
## Residual standard error: 0.944 on 21 degrees of freedom
## 
## F-statistic: 1.83 on 3 and 21 DF, p-value: 0.172
## 
## ------------------------------
## Q-Statistics for instrument strength:
## 
##   exposure1 exposure2 exposure3
## Q  1509.472   1009.18  1682.966
## 
## ------------------------------
## Q-Statistic for instrument validity:
## 
## 18.66954 on 20 DF , p-value: 0.5433899

initial Egger-MVMR:

## 
## Multivariable MR-Egger method
## (variants uncorrelated, random-effect model)
## 
## Orientated to exposure : 1 
## Number of Variants : 24 
## ------------------------------------------------------------------
##     Exposure Estimate Std Error  95% CI       p-value
##   exposure_1    0.298     0.489 -0.661, 1.257   0.542
##   exposure_2    0.077     0.208 -0.332, 0.485   0.713
##   exposure_3    0.456     0.221  0.022, 0.889   0.039
##  (intercept)   -0.002     0.009 -0.019, 0.015   0.787
## ------------------------------------------------------------------
## Residual standard error =  0.966 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic = 18.6538 on 20 degrees of freedom, (p-value = 0.5444)

pleiotropy MVMR test

## Q-Statistic for instrument validity:
## 18.66954 on 20 DF , p-value: 0.5433899

Testing Outlier with Radial test

## 
## Radial Multivariable MR
## 
##             Estimate Std. Error   t value   Pr(>|t|)
## exposure1 0.17763275  0.1899744 0.9350351 0.36039864
## exposure2 0.08922646  0.1919340 0.4648810 0.64680086
## exposure3 0.45932468  0.2084595 2.2034241 0.03886521
## 
## Residual standard error: 0.944 on 21 degrees of freedom
##           snp        wj corrected_beta          qj       qj_p ref_exposure
## 1  rs10245306 0.6012270    0.365023862 0.021112344 0.88447332   Exposure_1
## 2  rs10938397 0.6900585   -0.095682225 0.051548109 0.82039102   Exposure_1
## 3  rs11165643 0.5916230   -0.546195534 0.309967507 0.57770012   Exposure_1
## 4     rs11538 0.5892857    3.490799048 6.468631088 0.01097951   Exposure_1
## 5  rs12881629 1.3006135   -0.104882179 0.103808054 0.74730681   Exposure_1
## 6  rs13107325 0.4912281   -0.292436186 0.108544113 0.74180777   Exposure_1
## 7  rs13174863 0.6596859    0.520861675 0.077715017 0.78041817   Exposure_1
## 8   rs1421334 0.6666667   -1.954076029 3.029454869 0.08176548   Exposure_1
## 9   rs1503526 2.1840491   -0.031958752 0.095942210 0.75675458   Exposure_1
## 10  rs1884389 0.8421053   -1.099481102 1.373490344 0.24121310   Exposure_1
## 11  rs2237403 1.3874346    0.564257768 0.207392200 0.64881909   Exposure_1
## 12  rs2307111 0.5238095   -2.410850896 3.509653490 0.06101222   Exposure_1
## 13  rs3754963 0.8711656    0.946464646 0.514948181 0.47300464   Exposure_1
## 14  rs3803286 1.0584795    0.841980693 0.467168614 0.49429263   Exposure_1
## 15   rs429343 1.2146597    0.931269123 0.689887574 0.40620262   Exposure_1
## 16  rs4482463 0.6845238   -1.496726863 1.919048881 0.16596155   Exposure_1
## 17  rs4722398 2.0306748    0.068221904 0.024308665 0.87610210   Exposure_1
## 18   rs543874 0.9239766   -0.051108594 0.048344859 0.82596878   Exposure_1
## 19  rs7124681 1.0785340    0.259645857 0.007254382 0.93212413   Exposure_1
## 20  rs7206608 0.7857143    2.386694686 3.834250084 0.05021545   Exposure_1
## 21  rs7498665 0.9079755    0.322885291 0.019156740 0.88991807   Exposure_1
## 22  rs8027205 0.5263158   -1.529725300 1.534248158 0.21547599   Exposure_1
## 23  rs9304665 1.0471204   -0.508355962 0.492754459 0.48270117   Exposure_1
## 24  rs9367368 0.9047619    1.476836532 1.527175193 0.21653689   Exposure_1
## 25 rs10245306 0.6129466   -0.094581708 0.020708673 0.88557542   Exposure_2
## 26 rs10938397 0.6597018    0.375118248 0.053920138 0.81637716   Exposure_2
## 27 rs11165643 0.6377382    0.760714341 0.287553595 0.59179253   Exposure_2
## 28    rs11538 0.6498750   -2.915046007 5.865546284 0.01544007   Exposure_2
## 29 rs12881629 1.3545337   -0.182042326 0.099675743 0.75221910   Exposure_2
## 30 rs13107325 0.6645439    0.436699470 0.080235359 0.77697871   Exposure_2
## 31 rs13174863 0.8916492    0.343164072 0.057497385 0.81049607   Exposure_2
## 32  rs1421334 0.6163036    2.395134214 3.277015862 0.07025656   Exposure_2
## 33  rs1503526 1.9335460   -0.147518937 0.108372128 0.74200511   Exposure_2
## 34  rs1884389 0.8091754   -1.239860215 1.429385263 0.23186479   Exposure_2
## 35  rs2237403 1.2861204    0.506307868 0.223729521 0.63621279   Exposure_2
## 36  rs2307111 0.7278929   -1.773509753 2.525632592 0.11200985   Exposure_2
## 37  rs3754963 0.8709202   -0.679822072 0.515093278 0.47294229   Exposure_2
## 38  rs3803286 0.9734035    0.811638797 0.507999418 0.47600618   Exposure_2
## 39   rs429343 1.4648691   -0.535683790 0.572050170 0.44944538   Exposure_2
## 40  rs4482463 0.7287500    1.661972970 1.802586141 0.17940016   Exposure_2
## 41  rs4722398 1.7669080    0.214970331 0.027937502 0.86725584   Exposure_2
## 42   rs543874 1.0799064    0.284939387 0.041364249 0.83883645   Exposure_2
## 43  rs7124681 0.9221623   -0.006693672 0.008484513 0.92660952   Exposure_2
## 44  rs7206608 0.7777560    2.320892472 3.873483780 0.04905460   Exposure_2
## 45  rs7498665 0.7009325   -0.098931090 0.024815299 0.87482817   Exposure_2
## 46  rs8027205 0.5343813    1.770815096 1.511091520 0.21897261   Exposure_2
## 47  rs9304665 0.9519215   -0.665366024 0.542033429 0.46159123   Exposure_2
## 48  rs9367368 0.9107976    1.379820625 1.517054840 0.21806573   Exposure_2
## 49 rs10245306 0.5628736    0.659484343 0.022550908 0.88063081   Exposure_3
## 50 rs10938397 1.1795088    0.619224557 0.030157648 0.86213301   Exposure_3
## 51 rs11165643 0.7683874    1.016639209 0.238660745 0.62517507   Exposure_3
## 52    rs11538 0.7237262   -2.238382822 5.267008354 0.02173333   Exposure_3
## 53 rs12881629 0.8877423    0.873231631 0.152087100 0.69654878   Exposure_3
## 54 rs13107325 1.8932456    0.337358960 0.028163232 0.86672564   Exposure_3
## 55 rs13174863 0.6745131    0.795008705 0.076006676 0.78278381   Exposure_3
## 56  rs1421334 0.6726369    2.572112679 3.002565820 0.08313276   Exposure_3
## 57  rs1503526 0.6979571   -0.196529601 0.300222620 0.58374289   Exposure_3
## 58  rs1884389 0.4071462   -2.182144893 2.840806203 0.09189809   Exposure_3
## 59  rs2237403 0.3584445   -1.037188480 0.802754968 0.37027095   Exposure_3
## 60  rs2307111 1.0206012    1.787828303 1.801281382 0.17955766   Exposure_3
## 61  rs3754963 0.7043067   -0.491652918 0.636945712 0.42481897   Exposure_3
## 62  rs3803286 0.6779649   -0.577895231 0.729371693 0.39308692   Exposure_3
## 63   rs429343 0.5823455   -1.112614398 1.438971456 0.23030585   Exposure_3
## 64  rs4482463 1.2564048    1.371561761 1.045550519 0.30653407   Exposure_3
## 65  rs4722398 0.8799755    0.711806542 0.056095877 0.81277651   Exposure_3
## 66   rs543874 1.7639942    0.339510419 0.025322941 0.87356501   Exposure_3
## 67  rs7124681 1.1652513    0.535234421 0.006714515 0.93469272   Exposure_3
## 68  rs7206608 0.6052143   -2.408571151 4.977782477 0.02567487   Exposure_3
## 69  rs7498665 1.4237055    0.366689124 0.012217309 0.91198752   Exposure_3
## 70  rs8027205 0.4052316   -1.758196232 1.992685350 0.15806039   Exposure_3
## 71  rs9304665 0.6218063    1.614528159 0.829797431 0.36233111   Exposure_3
## 72  rs9367368 0.5425661    2.625825961 2.546657466 0.11052787   Exposure_3
##            q_statistic   p_value
## Exposure_1    26.43581 0.1903168
## Exposure_2    24.97327 0.2483238
## Exposure_3    28.86038 0.1173941

Run After deleting new outlier:

## 
## Multivariable MR
## 
##            Estimate Std. Error   t value    Pr(>|t|)
## exposure1 0.1079069  0.1512116 0.7136154 0.484615866
## exposure2 0.1271972  0.1557161 0.8168531 0.424692259
## exposure3 0.5016454  0.1702701 2.9461747 0.008637962
## 
## Residual standard error: 0.74 on 18 degrees of freedom
## 
## F-statistic: 3.31 on 3 and 18 DF, p-value: 0.0436
## 
## ------------------------------
## Q-Statistics for instrument strength:
## 
##   exposure1 exposure2 exposure3
## Q  1478.424  926.7414   1535.57
## 
## ------------------------------
## Q-Statistic for instrument validity:
## 
## 9.825719 on 17 DF , p-value: 0.9107591
## 
## Multivariable MR-Egger method
## (variants uncorrelated, random-effect model)
## 
## Orientated to exposure : 1 
## Number of Variants : 21 
## ------------------------------------------------------------------
##     Exposure Estimate Std Error  95% CI       p-value
##   exposure_1    0.471     0.526 -0.559, 1.501   0.370
##   exposure_2    0.078     0.220 -0.354, 0.510   0.723
##   exposure_3    0.514     0.231  0.062, 0.967   0.026
##  (intercept)   -0.007     0.010 -0.027, 0.012   0.454
## ------------------------------------------------------------------
## Residual standard error =  0.739 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic = 9.2963 on 17 degrees of freedom, (p-value = 0.9305)
## Q-Statistic for instrument validity:
## 9.825719 on 17 DF , p-value: 0.9107591

Sensitivity analyses with MendelianRandomization Package

## 
## Multivariable inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 21 
## 
## ------------------------------------------------------------------
##    Exposure Estimate Std Error  95% CI       p-value
##  exposure_1    0.108     0.204 -0.293, 0.508   0.597
##  exposure_2    0.127     0.210 -0.285, 0.540   0.546
##  exposure_3    0.502     0.230  0.051, 0.953   0.029
## ------------------------------------------------------------------
## Residual standard error =  0.740 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic = 9.8581 on 18 degrees of freedom, (p-value = 0.9364)
## 
## Multivariable MR-Egger method
## (variants uncorrelated, random-effect model)
## 
## Orientated to exposure : 1 
## Number of Variants : 21 
## ------------------------------------------------------------------
##     Exposure Estimate Std Error  95% CI       p-value
##   exposure_1    0.471     0.526 -0.559, 1.501   0.370
##   exposure_2    0.078     0.220 -0.354, 0.510   0.723
##   exposure_3    0.514     0.231  0.062, 0.967   0.026
##  (intercept)   -0.007     0.010 -0.027, 0.012   0.454
## ------------------------------------------------------------------
## Residual standard error =  0.739 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic = 9.2963 on 17 degrees of freedom, (p-value = 0.9305)